Well the Hornet is easily capable into the 2020's (as OTL) and boeing will still make parts so it isn't absolutely urgent. As its mentioned the ship design has some growth room they can probably mix in a few Super hornets then use whatever alt F-35 comes along in the late 2010's. By that point it will be time to build a replacement class(assuming a forty year lifespan as the Indy's would have had minus the defence review) so possibly the Tempest will have a carrier version in this universe.That would be my fear, too. No, I think the Hornet really is the better fit for what they're designing.
The real question is what they'd follow on with once Hornet production lines are shut down, and by that time, the Tomcats won't be an option, either.
In terms of a sea Typhoon the timing is wrong, during development the Hornets will be all but brand new and so there is no reason to develop an expensive new bird when there is no need for it. By the time the Hornet is approaching replacement the Eurofighter program will be near its end and building a 4.5 gen fighter when a 5th gen is only years away will be seen as pointless.
Also the TL has made no mention of FEFA and indeed the massive hornet buy seems to have replaced it so if there is a pan European fighter program the UK seems uninvolved.