I’ve been a few times to Croatia but always the islands (Vis) and never with a bike. From what I saw, it looks fantastic. Traveling in Europe, I usually go with a gravel/groad/allroad type bike with something between 32c to 38c tires because roads can be variable anywhere (Italy, Portugal, Greece, it’s not just Croatia). I traveled once with an MTB to Sintra, but it was an MTB focused trip.
First - absolutely bring your own Garmin, helmet and shoes. Preload Garmin maps from Openstreetmaps (DCRainmaker has a tutorial how to do this) before you get to Europe.
There are a whole bunch of courses, road and mountain, on Garmin Connect. Garmin Connect has been really my primary source for routes since I switched over after that Strava routes/military base controversy.
As for renting: look for Scott, Specialized, Cannondale, Trek dealers and call them on Monday. Getting access to these brands isn’t as easy as on the American market and I’ve never run into some BS Trek dealer, etc, like you sometimes do in the US. Some of them rent under the table if not outright and most of them will be helpful finding a good place to rent, most are excited to do so. Expect to pay between 25-50euros per day for a nice bike.
Also, if you’re having any problems finding shops or whatever, dig up some races (Croatia4Islands comes to my mind) and email the race organizers. They might not respond, but many of them work day jobs in tourism, region promotion or cycling.
And, lastly, get your partner a pedal assist e-bike for a day and do some easy scenic ride with them. I did this for the first time in Sintra with my wife and this transformed into an 80k ride around Lake Garda to her sometimes riding the trainer on her hardtail. Before that, she, honestly, could barely turn left on an MTB. It’s a great introduction to bikes and cycling and can really serve your selfish training purposes in the long-run
Some links: http://www.pedala.hr - only in Croatian, but you’ll Google Translate it
I think that’s all. Let me know if you have any questions. Be sure to eat a Cevapi at Kantun Paulina in Split and drink lots of rakija.