Careful, admitting that this came from 4e might not be wise. Lotta folks will turn up their nose just hearing the name. Though I appreciate that you did, in fact, mention it.
is the total modifier applied for HPs after 1st level?
this could be nice application for not min-maxing your point buy:
15+1,15+1,15+1, 8,8,8
modifiers: +3+3+3-1-1-1, total 6
13+1,13+1,13+1,12,12,12
modifiers: +2+2+2+1+1+1, total 9
At least with the way 4e did it, yes, increasing your Constitution score after first level did in fact increase your total HP.
All right, so I have to admit this has gotten me to go down a rabbit hole of sorts. As I think about HP between classes, I can't help but feel odd about having 9th level casters put on the same tier (HP-wise) as rogues and monks. Additionally, if wizards and sorcerers are given a the lowest tier of d6 HD because of their spell lists, then what of the bard that can now access all wizard spells by 10th level?
I find myself going back and forth on how to resolve this issue. Do rogues and monks move up to the next tier? Do all full casters move down a tier? I also feel like maybe fighters should move up to the same tier as barbarians.
In 4e, Wizards and other relatively squishy/"glass cannon" types (e.g. Invoker, Assassin, and Psion) got 4 HP per level after first, which means they had effectively d6 HP, average roll rounded up. The vast majority of classes, including Rangers, got 5 HP/level, equivalent to d8. Fighters, Paladins, and most other tanky-type classes got 6 HP/level, equivalent to d10; this is one of the (subtle) ways that shows that the Avenger, despite wearing cloth and being mostly a speedster, was in fact able to moonlight as a Defender because they had high HP and could get high AC via feats.
The only class that had more HP per level was Warden, which got 7 (equivalent to average d12, rounded up). Barbarians did not get bigger hit dice, and instead got various forms of self-healing, THP, or otherwise high self-sustain instead of having a bigger raw health pool per se. (Also, in general, Primal classes loved boosting CON, so they tended to have a lot of health regardless.)
Keep in mind that you DON'T add your constitution modifier to each level's HP, so the Wizard is gaining only 2/3 of the HP the Paladin or Fighter is, and only 80% of a Warlock or Ranger's gained HP. It may not seem like much, but they definitely still start out behind and, without intentional investment, they'll always be outstripped.
The absolute maximum HP a character can get (excluding taking feats or something) is being a Warden (17+Constitution at 1st level, +7 HP per level), starting with 20 Con and increasing it to 30 by the time you hit max level. For convenience, I'll treat it as "10+Constitution" base HP + 7xlevel gained XP, for a total of 40+210 = 250 HP. Toughness only adds an additional +15 HP, so realistically, the maximum total HP a level 30 Warden could have is 265. The minimum possible HP for a 4e character is a level 30 Wizard who started with 8 Constitution (which naturally increases by +1 at level 11 and 21, for a total of 10); they would have 18 (base HP) + 29x4 = 134 HP.
For comparison, a 20th level 5e Barbarian today, who maximizes Con and grabs Tough, has 12+7 (Con mod)+2 (Tough) = 21 HP from first level, and 7+7+2 = 16 additional HP per level thereafter, capping out at a whopping 325 HP. Meanwhile, the weakling 5e Wizard (-1 Con mod, so 5 HP at first level and 3 HP thereafter) caps out at a measly 62.
There's still plenty of space between the stoutest and flimsiest characters in 4e--it's just not the absolute ridiculousness (over 250 HP!) you find in 5e. Oh, and those 5e numbers scale dramatically faster, since we're looking at 30 levels of 4e vs only 20 levels of 5e. If you confine things to only the first 20 levels, the Warden up there won't even crack 200 HP. In other words: HP scale
dramatically faster in 5e than they ever did in 4e. You start off incredibly flimsy, but as long as you didn't neglect your Con mod, you'll almost surely grow well past not just an equal-level 4e character, but a
higher-level one.