I don't think one takes into account investment accounts with envelope budgeting, if I'm not wrong. All the accounts in this kind of budgeting should be involved in the budget, to be money that is to be assigned. "Give every dollar a job" kind of style. Money in investment accounts is for the most part saving for savings sake. But I guess people can assign that kind of money as well, e.g. "this is money that I'm investing to be able to buy a house in 5 years". I'm not an expert on this so you could look up how YNAB does it, or if Actual has any docs on this.

Nope, which honestly annoys me but is pretty par for the course. That said, when it comes to budgeting, I mostly care about where money is going and care less about the "whole financial picture." If I need to estimate what retirement looks like, I want more than a simple budgeting tool.

I personally use Fidelity for investment tracking. My main "checking" is their Cash Management Account, my "savings" is a brokerage account (invested in t-bills and money market funds), and I can link all of my other accounts and it pulls in specific investments and shows a consolidated view. It's awesome because it shows all kinds of stuff, like morningstar-style factor weights, sector exposure, etc. It's not self-hosted, but I trust them with my banking anyway, so it's not like I'm opening myself up to some new exploit (oh, and Fidelity also has proper MFA; Symantic VIP, which kinda sucks, but it's way better than any other financial institution).

I used to track this stuff via a Google spreadsheet (couldn't find a way to get stock quotes in LibreOffice), but this seems to be good enough for me.

As others said, both Firefly III and Actual Budget do not support stocks. I wish they did, but I guess I'll have to stick with GnuCash + Metabase for now.