Why did my fresh pasta come out pasty and lumpy?

1. Sounds over cooked. Fresh pasta and noodles don't take so long to cook as dried noodles of the same size.

2. Might be the flour. If in doubt, try a different brand. Though semolina is the traditional flour for Italian pasta, just about any flour will make a pasta or noodle of some kind, though with varying textures and flavours. You can pay around with flour mixes and find one that suits you.

Fresh pasta cooks in just a few minutes, so taste it early. It should be al-dente just like properly cooked dried pasta. Let your fresh pasta dry (I hang mine over the back of a chair) for half an hour or longer before you cook it, so that there's some crunch for the al-dente feel.

Most recipes advise "type 00" flour, which is milled extra fine. You should be able to tell when you've kneaded enough - it just needs to feel perfectly smooth in your hands. You don't need to knead for ages like bread dough, but you do need to have mixed the liquid and the flour completely thoroughly.

You've already good answers about the second part of your question (lumpy texture), but I don't think that people thoroughly answered the first part:

I know how to tell when boxed pasta is done, but I'm not sure what the texture of fresh pasta should actually be like. Should it be similar to that of "Al dente" boxed pasta? Mine was weirdly soft and I'm not sure if it was under or over-cooked.

No, it should not be similar to "al dente" dried pasta. It's always going to be "weirdly soft", even when it's cooked correctly, if you're comparing it to properly cooked dried pasta. It has a silkier, softer texture.

Fresh and dried pasta are basically two different ingredients, sort of how fresh and sun-dried tomatoes, or fresh and dried herbs don't cook up the same way.

Usually it only needs a minute or two in rapidly boiling water (do not try to start it in cold water), with thicker or semi-dried pastas (made earlier in the day) taking a little bit longer than stuff you just rolled out.

I would recommend that you ask around, and see if any of your friends (or their parents or grandparents) make fresh pasta, and see if you can watch them, or at least sample their finished product, so you know what it's supposed to end up like.

You could also try checking to see if any restaurants near you serve fresh pasta, and try it there. (although if you're currently under a lockdown / takeout only situation, I would wait, as the texture is going to suffer). And it doesn't need to be an Italian restaurant -- there are plenty of fresh asian noodles, or even pick apart a dumpling made with fresh pasta so you can get a sense of just the wrapper texture.

And if even that's not an option, you can try looking through the refrigerated or freezer section of your grocery store to see if they have prepared fresh noodles, so you can compare that to your attempt. If you don't see any, ask -- I've seen it tucked away in the cheese case before.