Given the uncertainty, this is what I'd do.
1. Run Cat 6 cables for ceiling-mounted wireless access points (a) near, but not in front of, the fireplace in the family room, (b) to the hallway to the master bedroom, and (c) in front second family room folding doors.
2. Run a Cat 6 cable to a wall jack in the office. You want at least one hard-wired connection to your network equipment (modem, switch if any, etc.) and don't want to rely on wi-fi.
3. Skip the Cat 6 cable to the doorbell. A quick search shows that the video doorbells use wi-fi, not a wired network. DO install the typical doorbell copper wiring, transformer, and doorbell (ding-dong). The video doorbells are designed for retrofit and are powered by the standard doorbell transformer.
4. I have no opinion on the coax. More and more people are using smart TVs, computers, or phones that are connected solely to their home networks (hard-wired or wi-fi).
Q
shower seat
Q