Same issue here. It also works if you remove/rename steamclient64.dll from your Steam folder before launching the game.

Here's a dump of the process when it's hanging, not that it's super helpful. Seems like there's some issue with the way this game is using the steam API

Code:
*******************************************************************************
*                                                                             *
*                        Exception Analysis                                   *
*                                                                             *
*******************************************************************************

*** ERROR: Symbol file could not be found.  Defaulted to export symbols for steamclient64.dll - 
*** ERROR: Symbol file could not be found.  Defaulted to export symbols for steam_api64.dll - 
*** ERROR: Symbol file could not be found.  Defaulted to export symbols for ffxiv_dx11.exe - 
*** ERROR: Symbol file could not be found.  Defaulted to export symbols for nvwgf2umx.dll - 
*** ERROR: Symbol file could not be found.  Defaulted to export symbols for nvcuda64.dll - 
GetUrlPageData2 (WinHttp) failed: 12007.

DUMP_CLASS: 2

DUMP_QUALIFIER: 400

FAULTING_IP: 
+0
00000000`00000000 ??              ???

EXCEPTION_RECORD:  (.exr -1)
ExceptionAddress: 0000000000000000
   ExceptionCode: 80000003 (Break instruction exception)
  ExceptionFlags: 00000000
NumberParameters: 0

FAULTING_THREAD:  00003b08

DEFAULT_BUCKET_ID:  STATUS_BREAKPOINT

PROCESS_NAME:  ffxiv_dx11.exe

ERROR_CODE: (NTSTATUS) 0x80000003 - {EXCEPTION}  Breakpoint  A breakpoint has been reached.

EXCEPTION_CODE: (HRESULT) 0x80000003 (2147483651) - One or more arguments are invalid

EXCEPTION_CODE_STR:  80000003

WATSON_BKT_PROCSTAMP:  63178c27

WATSON_BKT_PROCVER:  1.0.0.0

PROCESS_VER_PRODUCT:  FINAL FANTASY XIV

WATSON_BKT_MODULE:  unknown

WATSON_BKT_MODVER:  0.0.0.0

WATSON_BKT_MODOFFSET:  0

WATSON_BKT_MODSTAMP:  bbbbbbb4

BUILD_VERSION_STRING:  10.0.19041.1889 (WinBuild.160101.0800)

MODLIST_WITH_TSCHKSUM_HASH:  b0d60123200cf4e76ec3dd1569c915c388da025b

MODLIST_SHA1_HASH:  95f5d70f4f62623e6a543bf52be81a8c28c8dcc0

NTGLOBALFLAG:  0

APPLICATION_VERIFIER_FLAGS:  0

PRODUCT_TYPE:  1

SUITE_MASK:  272

DUMP_FLAGS:  8000c07

DUMP_TYPE:  0

ANALYSIS_SESSION_HOST:  

ANALYSIS_SESSION_TIME:  10-01-2022 18:49:11.0738

ANALYSIS_VERSION: 10.0.14321.1024 amd64fre

THREAD_ATTRIBUTES: 
OS_LOCALE:  ENU

PROBLEM_CLASSES: 




    Tid    [0x0]
    Frame  [0x00]
    String [STATUS_BREAKPOINT]
    Data Bucketing


BUGCHECK_STR:  STATUS_BREAKPOINT

LAST_CONTROL_TRANSFER:  from 00007ff830a5af23 to 00007ff83332d244

STACK_TEXT:  
00000058`5a18edd8 00007ff8`30a5af23 : 00000002`00000001 00000001`00000002 00000000`00000000 00007ff8`30a93a7b : ntdll!NtReadFile+0x14
00000058`5a18ede0 00007fff`b8f1f0c0 : 00000001`0001b000 00000000`00000000 00000001`00000001 00000058`5a18f2b0 : KERNELBASE!ReadFile+0x73
00000058`5a18ee60 00007fff`b8f1c181 : 00000000`00000000 00000000`0002bf00 000001de`00000000 000001de`6d100440 : steamclient64!Steam_TerminateGameConnection+0x384f20
00000058`5a18f2b0 00007fff`b8f1c4c0 : 000001de`6d190144 000001de`6d100440 00000058`5a18f480 00000000`00000000 : steamclient64!Steam_TerminateGameConnection+0x381fe1
00000058`5a18f2f0 00007fff`b8f00b41 : 00000000`00000001 00000000`00000001 000001de`6d190000 00000000`00000040 : steamclient64!Steam_TerminateGameConnection+0x382320
00000058`5a18f450 00007fff`b8dd90b4 : 000001de`6d0912c0 00000000`00000000 00000058`5a18f7a0 00007fff`b97fcf48 : steamclient64!Steam_TerminateGameConnection+0x3669a1
00000058`5a18f770 00007fff`b8d909dc : 00000000`00000001 00000000`0af949a4 000001de`00000000 00000000`0000000b : steamclient64!Steam_TerminateGameConnection+0x23ef14
00000058`5a18f800 00007ff8`013f719a : ffffffff`00000000 00000000`00000000 000001de`67521780 00000000`00000001 : steamclient64!Steam_TerminateGameConnection+0x1f683c
00000058`5a18f880 00007ff8`013f8170 : 00000000`00000000 00000000`00000000 00000000`00000000 00000000`00000000 : steam_api64!SteamAPI_SetTryCatchCallbacks+0x222a
00000058`5a18f8b0 00007ff6`2620d828 : 000001de`6ae4cc00 00000000`00000000 00000000`00000005 000001de`7516b1f0 : steam_api64!SteamAPI_RunCallbacks+0x70
00000058`5a18f8e0 00007ff6`25c92908 : 000001de`6757df90 00000000`00000000 00000000`00000000 000001de`67521780 : ffxiv_dx11+0x60d828
00000058`5a18f910 00007ff6`25c562b5 : 00000007`3f86c8e2 00000000`00000006 00000000`00000001 00000000`00000000 : ffxiv_dx11+0x92908
00000058`5a18f940 00007ff6`25c59907 : 00000058`5a18fab0 00000000`00000000 00000000`00000000 00000000`00000000 : ffxiv_dx11+0x562b5
00000058`5a18f9b0 00007ff6`2715720f : 00000000`0000000a 00000000`00000000 00000000`00000000 00000000`00000000 : ffxiv_dx11+0x59907
00000058`5a18fee0 00007ff8`32e27034 : 00000000`00000000 00000000`00000000 00000000`00000000 00007ff8`00770000 : ffxiv_dx11+0x155720f
00000058`5a18ff20 00007ff8`332e26a1 : 00000000`00000000 00000000`00000000 00000000`00000000 00000000`00000000 : kernel32!BaseThreadInitThunk+0x14
00000058`5a18ff50 00000000`00000000 : 00000000`00000000 00000000`00000000 00000000`00000000 00000000`00000000 : ntdll!RtlUserThreadStart+0x21


STACK_COMMAND:  ~0s; .ecxr ; kb

THREAD_SHA1_HASH_MOD_FUNC:  381c0ac413399062e171a3713d2c20f1741b0dff

THREAD_SHA1_HASH_MOD_FUNC_OFFSET:  3a07856cd4950014a52192315fd8f790150af6de

THREAD_SHA1_HASH_MOD:  b7c652e4258c3e4bce98b15e467582dae73ae68f

FOLLOWUP_IP: 
steamclient64!Steam_TerminateGameConnection+384f20
00007fff`b8f1f0c0 85c0            test    eax,eax

FAULT_INSTR_CODE:  7674c085

SYMBOL_STACK_INDEX:  2

SYMBOL_NAME:  steamclient64!Steam_TerminateGameConnection+384f20

FOLLOWUP_NAME:  MachineOwner

MODULE_NAME: steamclient64

IMAGE_NAME:  steamclient64.dll

DEBUG_FLR_IMAGE_TIMESTAMP:  63339b1a

BUCKET_ID:  STATUS_BREAKPOINT_steamclient64!Steam_TerminateGameConnection+384f20

PRIMARY_PROBLEM_CLASS:  STATUS_BREAKPOINT_steamclient64!Steam_TerminateGameConnection+384f20

FAILURE_EXCEPTION_CODE:  80000003

FAILURE_IMAGE_NAME:  steamclient64.dll

BUCKET_ID_IMAGE_STR:  steamclient64.dll

FAILURE_MODULE_NAME:  steamclient64

BUCKET_ID_MODULE_STR:  steamclient64

FAILURE_FUNCTION_NAME:  Steam_TerminateGameConnection

BUCKET_ID_FUNCTION_STR:  Steam_TerminateGameConnection

BUCKET_ID_OFFSET:  384f20

BUCKET_ID_MODTIMEDATESTAMP:  63339b1a

BUCKET_ID_MODCHECKSUM:  151ef85

BUCKET_ID_MODVER_STR:  7.53.93.61

BUCKET_ID_PREFIX_STR:  STATUS_BREAKPOINT_

FAILURE_PROBLEM_CLASS:  STATUS_BREAKPOINT

FAILURE_SYMBOL_NAME:  steamclient64.dll!Steam_TerminateGameConnection

FAILURE_BUCKET_ID:  STATUS_BREAKPOINT_80000003_steamclient64.dll!Steam_TerminateGameConnection

WATSON_STAGEONE_URL:  http://watson.microsoft.com/StageOne/ffxiv_dx11.exe/1.0.0.0/63178c27/unknown/0.0.0.0/bbbbbbb4/80000003/00000000.htm?Retriage=1

TARGET_TIME:  2022-10-01T22:48:20.000Z

OSBUILD:  19044

OSSERVICEPACK:  1889

SERVICEPACK_NUMBER: 0

OS_REVISION: 0

OSPLATFORM_TYPE:  x64

OSNAME:  Windows 10

OSEDITION:  Windows 10 WinNt SingleUserTS

USER_LCID:  0

OSBUILD_TIMESTAMP:  2011-03-01 17:27:29

BUILDDATESTAMP_STR:  160101.0800

BUILDLAB_STR:  WinBuild

BUILDOSVER_STR:  10.0.19041.1889

ANALYSIS_SESSION_ELAPSED_TIME: 19db

ANALYSIS_SOURCE:  UM

FAILURE_ID_HASH_STRING:  um:status_breakpoint_80000003_steamclient64.dll!steam_terminategameconnection

FAILURE_ID_HASH:  {f19f7334-0e4c-ee40-78e6-09f7dba5b83e}

Followup:     MachineOwner