Well DICE isn't developing their BR mode and EA has never done a full on GaaS before, not to mention that both Battlefield 3, 4, and 1 had incredible post launch support, so not sure what you're talking about when it comes to the whole "EA isn't known for their loving support" because EA isn't the one supporting these games, it's DICE and their sister studio.
Isnt DICE fully owned by EA, and are basically like any other EA developed games in that regards? If so, you're right that DICE is the one supporting the games that they develope, but i dont think they can do this without EA's approval, so EA would be the one supporting the games further on in that case (paying the developers and says its ok that they work on further updates for a game instead of moving them to a new project).
They will support it until the next Battlefield comes out.
As for Apex thing, i bet they will drop it as soon as the playerbase starts to slow down, i don't trust EA on committing to it the same way Epic is doing with Fortnite, not to mention the game seems less accessible (no mobile and no Switch, you're missing a big piece of the audience for these games), it won't reach nowhere near the same success.
Its a bit difference with what happened to Fortnite though. Fortnite launched on PS4/Xbox One/PC and kept on growing in popularity once the Battle Royale mode was added. Then Epic Games decided to build on this momentum, making the game for Switch and mobile as well. From what i know, it wasnt a case where Fortnite was dropping in popularity, and Epic Games felt they had to make a Switch and mobile version to stop the decline.
If Apex takes off like Fortnite did, who knows if EA will expand to other platforms. Thats what happened with Fortnite and PUBG. PUBG on mobile is also basically like a seperate game from what i know (no cross play with PC or consoles i think due to the differences). I dont think it can be expected that a brand new game like Apex should be ready for PC/PS4/Xbox One/Switch/mobile all at the same day. Its technically possible, but it also require a lot of more work and investment. If the game cant stay popular on PC/PS4/Xbox One, i'm not sure if adding a Switch and mobile version will change much.