Cheaper to book local flights in Italy vs booking through Delta - do I need to go back through security?

I need to book a flight to land in Brindisi. I will be flying out of Rome to go back home at the end of my trip. I compared prices and it seems to be cheaper to just book round trip through Delta to/from Rome and then book a separate flight through an Italian airline to Brindisi on my arrival day. My flight would land in Rome just before 7 am and the Brindisi flight departs at 9:40 am. Would this be enough time? I’m wondering if I’d have to go through customs, then to baggage claim to get my bag from Delta and then have to go through security etc to be able to board my flight to Brindisi? Would that be enough time? And would it be worth it to just pay the difference and book fully through and have my checked bag be moved for me to my final destination? I’m assuming I wouldn’t have to go through security etc. and then grab my checked bag until I arrived in Brindisi if I did it this way? Never booked local flights like this before so any advice would be appreciated!