The older ones defined the genre. They're still fun to play albeit a little dated. No idea how good the Switch ports are.
Doom 3 is slower and more focused on horror than the others. It's a good horror fps but not a good Doom game.
Doom 2016 is the first of the modern Doom games. Fast, brutal, super fun through and through. If in doubt start with that one.
Doom Eternal is the second of the modern Doom games. It's even faster than 2016. But it has more focus on using every mechanic at your disposal. Learning those mechanics is a little bit tedious at first. But once everything is available it's an adrenaline pumping high speed 4D chess. When you've mastered everything every fight lets you enter a trance of violence that's absolute bliss.
Metroid Prime series are more "action games" than FPS' per se, but they are must-plays if you haven't, & might scratch that itch. There's a switch remaster of the first game, none yet for Prime 2 or 3 but it's likely they'll come out leading up to the release of the recently-announced Prime 4
BPM: Bullets Per Minute. A boomer shooter had an affair with he rhythm game genre and this was the outcome. Amazing game, assuming you don't mind rhythm games, and an immaculate one if you actively like rhythm games.
Neon White is technically a shooter, but in most ways does not play or feel like one. It's better described as a first person puzzle/platformer, but I would still recommend it, as it is an incredible game.
Both of the Doom ports run insanely well on the Switch. Seemingly impossibly well considering how dated the console is.
Warframe is good, free and playing surprisingly well on Switch.
Plants vs Zombies Battle for the Neighborville. You might think I'm kidding, but in terms of how it feels to play it's my favorite shooter on the switch. The people who made that knew what the fuck they were doing.
I don't play anymore, but I sank over 1500hrs into it. They've had several content updates since then, too, so there should be plenty to keep you busy.
Word of advice for starting: focus on opening up every planet in your star chart. After that, you should have access to every mission and event.
This might not be exactly what you're looking for, but Neon White is one of my favorite games of the last few years, and it's on the Switch. I played on PC, but I haven't seen any complaints about the Switch version.
I don't really know if I'd call if a first person shooter. It's more like a first person platformer and you have to shoot some targets before completing the level. Levels are very, very short, and you'll replay them many times to shave a fraction of a second off of your time.
I have not played it yet personally, but they have the turok trilogy bundle on the switch. I've heard those games are good. The serious Sam collection is also available and that's a lot of fun