Like @devtoi@feddit.nu I use plain-text accounting (PTA) to manage a few bank accounts, including small businesses. In my case, I'm using hledger. Every time I get a receipt, invoice, or statement, I type it into a text file. My bank gives me CSVs which are easy to import. Reports are done with a few commands; repeatable reports are done by saving commands to a shell script. hledger comes with builtin tools for monthly reports, BSE, currencies, pending invoices, closing/opening new years, and those are merely what I recall using recently.

I have been satisfied with beancount. https://github.com/beancount/beancount and fava as a ui. It's text based so it is easy to automate imports and exports. It can seem daunting at first to create importers in Python, but it's pretty basic scripting.

Text based accounting lends itself well to easy experimentation with version control.

I tried gnucash for a while, but it felt so slow and not flexible enough for me.

https://gnucash.org/

I use and like HomeBank

I haven't used it yet, but I want to start keeping better track of my finances and one I've seen recommended a lot and plan to try out for February is Actual Budget.

I used to use You Need A Budget and was looking for an open source alternative. I've been using Actual since last year and I really like it so far. It has all the features I'd been looking for and is free and open source. It seems to fit your list of requirements as well! I'd highly recommend it!

Check out https://www.firefly-iii.org/

Oh crap - I forgot an important need: it has to be able to import my existing data (decades!) which Moneydance can export to QIF, tab delimited, or JSON.