Concern about gaps in unemployment.

Basically, after a staggered start (dropped out of uni), unemployed over COVID, went back to uni and now a 25 year old graduate I'm concerned my gaps in employment are hindering my chances. I worked when I could, temp work over COVID, summer work during my degree but I've struggled after graduating last year. I spent a lot of time after graduation applying for grad schemes etc. and I've actually got on one that was due to start this month but it's now been pushed back to September and tbh it's left a bad taste in my mouth and I'm looking for something else to at least give myself a dilemma come September. I haven't had a consistent job for longer than 3 months since I was 18 and since I was sure I was starting this grad scheme the only work I've been doing is 'self-employed' courier work and I also had a stint at Waterstones over Christmas. I'm applying for jobs now pretty religiously, anything I can get tbh, retail, supermarket, temp office work with agencies and also longer term jobs in stuff like the civil service. I'll be honest, I've had immense support from my parents, maybe too much which led me to be pickier than I should've been in the past, however, I've spun my unemployment quite well but I just want reassurance that my previous inaction hasn't absolutely cooked my chances of getting something decent as I've still got myself a good degree and some experience.