Do cocktail onions need to be pressure canned I've decided that the cocktail onions I can buy pale in comparison to some that I've had in better establishments.  They're tiny and lack crunch, even when I try to buy something top-notch.

So, I think I'd like to try my hand at making them.  There are a ton of recipes out there, like https://www.marthastewart.com/1144099/cocktail-onions.  I've never done any canning before, and it's a bit intimidating, so I'm reading up on this.

Now, I've come across things that say since onions are low-acid, they should be vacuum canned. Do I need to do that for pickled cocktail onions, even though the recipes I've seen don't say to?  Does the acidic pickling have anything to do with this?  If I do need to vacuum can, will that make the onions mushy?
In canning, you can't make up your own recipes. There are too many "gotchas" which you cannot predict or measure. So while in principle yes, acid will make a low-acid food cannable in a water bath, just taking a recipe meant for other use and canning it is not safe. And you have to follow it exactly - if the recipe is for cut-up onion for example, you cannot use whole onions. 

There likely are recipes for canning pickled onions, look around for those, and try them out.