I applied for a funded PhD project at Imperial on the 2rd of April. Deadline was 7th of April. I only got invited for the interview on the 26th of April. This seems late to me - usually, I get invited to interview 1-2 weeks after the deadline and decisions usually get made really quickly. I've applied for a studentship and they had picked a candidate within 3 weeks. So 3 weeks for an interview seems like they don't really want me.

Does being invited to interview mean I could still stand a chance for the project? The late invite gives me the impression that they've interviewed their top candidates already and they're just inviting me cos they're bored or kinda interested in me but don't have any intention of giving it to me.

Thoughts? Should I even bother going?

They wouldn't waste their own time interviewing you if they didn't think you had a chance as a candidate for the project. Three weeks isn't that long to wait for an interview offer, you're fine.

I agree with Bombus. There is always a chance they have someone else lined up for the funding - but it would be impossible to tell based on when they invite you to interview. Good luck!

I don't think that timeline is anything to be concerned about - sometimes decisions to interview do take this long.

The timeline is not of importance but lets not be naive about this. Employers absolutely DO interview "ghost candidates" from time to time. The reason for this apparent waste of time is very simple. It allows them to tick a minority quota box or to show evidence that they didnt just hire their friend without at least talking to another candidate.
I am not suggesting that this is what is happening here but it definitely happens.