On this topic. Do WiFi signals contain time (unencrypted)? If so why does my oven not pull time from the air and needs adjustment every 2 months? If not, why are APs not defacto time beacons for all sorts of non-smart appliances (and clocks)?
The gateway/router should be the time source. DHCP has an option to provide the time server (NTP) - option 42, and most decent devices or OSS/DIY router software (OpenWRT, opnSense) will support that as well as being the local time server.
I have thought that could use Matter for time sync. It works with both Wifi and Thread. I don't think there is a time message. I also don't know if it has public broadcast since Thread needs pairing to work.
The advantage is that smart devices might have Matter support already. People with Matter devices will have border routers, which are perfect place for running NTP and broadcasting time.