8 speed cassette increased from 25 to 30
With an old road bike it's impossible to tell just by looking. Many older derailleurs were designed when 28T was as big as it got, but they will still work with a 30T. But they might not, too.

If you're definitely going to make the change there's no real loss if you buy the cassette and try it. If the derailleur doesn't work, buy a new one. You might pay two lots of shipping, in which case the question is whether the second lot of shipping is enough to make it worth buying the derailleur anyway.

A better option would be to see if you can scrounge parts from a local bike co-op or tip shop. That way the cost is mostly your time, and if something doesn't work it doesn't take long to find a different one. Even if you end up running an MTB derailleur, the main thing is that it works.