That's how it worked in HOI3, and IIRC HOI2. The ships would automatically engage in shore bombardment in any coastal province where there was combat. It could be an amphibious landing, but also applied if you had ground forces attacking along the coast.
The mission then is to Hold in the coastal sea zone if they are not part of an invasion mission.
Except for carriers, which can Hold further out to sea, and you use the air map mode to give more specific missions to the different plane types in the CAG. Including port strike, bombing of ground forces or logistics strike.
The only obvious omission is the ability of a surface fleet without carrier support to attack ships in a port. It didn't happen very often IRL, and you can see why it might not be included, as it could be a complicated mechanic to get right.
I hope the arrival of any fleet just off the coast (either amphibious landing or shore bombardment) has an immediate response by the AI, naval and air. And the player gets informed.
Just checked my Steam-account, 475 hours of HOI3 since 2014-07-16 (holy crap that is a lot considering I haven't played it since 2015-03-15, but I blame Black Ice Mod
Note that I'm not being sarcastic or anything I'm just not a big fan of amphibious landings in HOI3 for several reasons so I never took the time to figure out the mechanics much, and also I have mostly just played mods where landings occur by events.