jphart is correct. It's an international flight so on the return flight you will need to clear immigration, collect your bag, clear customs then go back upstairs for the Agriculture scan before you recheck your bag and clear security. SJU used to have a bag check immediately after customs but I haven't seen it staffed in several years. My experience is the lines at SJU go very fast so it doesn't take much time but 1.5 hours would be a minimum for me.

I've gotten mixed responses from people regarding checking all the way thru on partner airlines. I don't have much Cape Air experience but they are the most professional interisland connection so they'll get it done if anyone can. I've done the SEA-EIS trip at least 40 times since 2017 but most of the time on 2 tickets and with carry-on so not much experience.

Enjoy!