this kinda works, but it's also kind of a pain after a certain depth. https://youtu.be/i7wDnM_zq0E

or you can just use the fly command
control lowers you
space raises you
you don't need air but you use and restore stamina normally
dig all you want and bust rocks underwater

of course that's a CHEAT

If you install mods, the mod valheim+ simply allows you to change settings to make everything float. And I mean everything. I ended up added that just for mistlands. Got tired of staring at loot in 6 feet of water.

Thank You!

If you jump off of something tall, you might be able to sink low enough in order to grab the item. Otherwise, you might be out of luck.

There's no mechanic to swim under the water, however if you jump from height you will plunge - if you're lucky you'll plunge deep enough.

you can also reach down quite a ways, maybe 5 or so meters at a rough guess. If jumping from a raised terrain, you are then able to recover stuff about 8m deep.
For deer ... learn the lesson (kill them on land) and let it go. There are too many deer for this to be worth recovering. Later if you must have that deer or whatnot, you can drag them back onto shore and into melee range with one of the weapons, but until then... let it go.

We all float down here. There are two mods that i know of that can help, one is called floating items and one is in valheim+.

If it's shallow enough, build a platform that lets you jump from above the loot. Once you have the goods, you can break the platform, and the wood will float.

If you have an actual boat already, either the karve (this moves pretty easily) or the longship, you can also sort of push yourself underneath the water a bit with that. The jump gets you to drop farther down, but i found wedging myself under my longship to be a decently effective way to place underwater supports for a dock to...though actually seeing what i was doing was an entirely different related issues.

Later on you may discover a way to drag things out of the water before murdering them (or drag them around in general) but that's really the only options you get for recovering underwater loot besides that some of it (like wood for example) floats. Otherwise its mods or console commands (console doesnt let you dive, but you can turn off the swim effect to run along the bottom for things like loot collection or building). Luckily, deer are plentiful so in this case it's not the biggest loss. Just have to wait a bit longer to find some more. Lesson learned for a relatively low cost, not a bad outcome in this game.

Thank you for the replies!

The other mod you can use is seafloor walking pants. Bonus: they're fantastic for digging canals.