Most likely June or July. They love June for release dates. Here's some history.
- 27 August 2013 (ARR)
- 23 June 2015 (Heavensward)
- 20 June 2017 (Stormblood)
- 2 July 2019 (Shadowbringers) (early access was 28 June)
- 7 December 2021 (Endwalker)
All but 2 of those are effectively June. We got access to all of these expansions a week before these dates due to early access. Endwalker would have probably been in summer as well but it suffered from the Covid-19 delays.
So it is very likely they are aiming for the favorite month of June and it would all line up to be then as well.
After 4.55, we got Shadowbringers 4 months later. If we applied that to now, it would release in May. But they have longer breaks and holidays and patch gaps now, so if we allow for an extra month it reaches their favorite month.