I believe @Xuanqian was referring to the iPhones with regards to checking wireless bands. You just need to go into Settings>Wi-Fi and confirm it’s actually on the 5g network.
I’m not sure with regards to the Time Capsule but it helps with wireless routers to have unique wireless names for 2.4g and 5g, that way you can see more easily which one the connected device is actually using.
If you have checked there is enough free space, reset network and restarted plus deleted LDS and reinstalled there are a couple of other things you could check.
Apple iDevices now throttle power when the battery ages which sometimes impacts processes and results in odd behaviour, go to Settings>Battery>Battery Health and see if “Maximum Capacity” is getting close to 80%, if it is you may be impacted by this process (you normally get a warning though and I think it can be turned off) and you may need to consider a replacement.
The other option is to use a Mac (or PC) and Restore the iPhone, but when asked setup a “New”. This is rather like taking a sledgehammer to crack a nut but it basically gets rid of every user configuration or installed app that can mess the device up. It can also sort out issues that can arise from numerous OTA updates. Once done only install LDS and see what happens.
(Note you use iTunes on a PC or Mac’s pre Catalina to do same).
Be aware you will loose all personal stuff stored on the iPhone but if you are syncing to iCloud a lot of that will come back when signed back in to your Apple ID (Mail, Contacts, Calendar, Notes, Photo’s etc), but it would be wise to have your own backup’s of such data just in case.
You can also restore the device from within Settings, but it doesn’t replace the existing iOS like when using the computer so could in theory leave some corruption behind.
I’m unsure with regards to the issue being the fault of the Time Capsule, after all it’s working fine on yours and you both run iOS13 and the devices are not that far apart with regards to performance or hardware, but that’s just my view.
Hope some of the above helps.