Both! Unicode has some support for as-is ligatures. For example fi is U+FB01.

Modern fonts can also use self-defined ligatures. That's how fonts like https://www.sansbullshitsans.com/

So my plan is (eventually) to add in ligatures where Unicode has defined them - and automatically replace typed text with self-defined ligatures where it doesn't.

Of course they do, better than ever actually. Google OpenType ligatures, for example. You can even use those on the web using CSS.

Some fonts have hundreds of different ligatures.

Yes, they do. Part of the OpenType standard are the so called “OpenType features” which (amongst other things) allow for contextual alternates, i.e. different kinds of ligatures, and for stylistic alternates, e.g. a slashed zero, a single-storey ɑ, etc. All of these different glyphs are encoded in the font and can be enabled when typesetting using different selectors. This website shows them off.

Some ligatures, like “ffl”, are a separate character in Unicode. Some were added because they can be considered a different character in languages other than English. Some (like “ffl”) were added because of legacy reasons; “no more will be encoded in any circumstances”.