If your actions are all crossed out, you can open Actions & Traits which is in the Character menu and drag the new actions onto the hotbar. You do have summons, but they only appear temporarily to cast their main attack and then imbue you with an element. The rest of the time you will have Carbuncle out, but you can change its glamour with /egiglamour Carbuncle Garuda-Egi or /egiglamour Carbuncle Ifrit-Egi.

Summoners in Final Fantasy games would typically call upon a summon to perform its main attack and then they would disappear, while a few more recent games have them appear as temporary pets. But whether you prefer one or the other, Summoner was neither of these because it spent a lot of time applying dots, casting Ruin and using baby versions of those summons called egis.

To make it the way most people see a Summoner, it was changed so that you summon it to do its main attack the same way as in many other Final Fantasy games, but after that you can use attacks of the same element as the summon.

Before level 90 they are still egis, but eventually they become larger versions.

The change was necessary because of complaints that Summoner had too many buttons and there wasn't much room for them to add more of them, so something needed to change.

Unfortunately, because it plays a lot differently now, people who enjoy dot classes are left unhappy but it was a less popular job before. The closest alternative for dots is bard.