[OFF TOPIC] Problems with Reverse Proxy on Synology NAS, Safari and devices on LAN

Not related to HA, but perhaps some network gurus could help…
So, I have a bit twisted setup of my network to be able to access most important devices or services on my LAN by FQDN. For these I did setup Reverse Proxy on Synology NAS to be able to call them by name and have additionally port translation if needed. I also have AdGuard Home running in docker on NAS to filter unwanted content. For all LAN devices NAS (AdGuard) is set up as DNS (so DNS queries are going to AGH, ar e filtered and then are redirected to Google DNS). So far it was working fine for both external and internal access.
Last week I made major change in my setup converting from Internet access from cable TV provider to FTTH. Unfortunatelly it turned out that NAT loopback is not working on provided router, so calls to my own domain from LAN are not returned back to Reverse Proxy/LAN :frowning:
After some tinkering I made small chnage, that almost solved the problem; in AdGuard Home I added DNS rewrite rule to redirect all my domain calls to IP of Reverse Proxy, so now these are returned back to LAN, before reaching the router. It works for 90% of devices only though…
For few devices (like my own router) when I enter the name of device I get redirected to default Synology error page, instead of web interface of device. Strangely, upon examination of address bar I see that there is www. prefix added to URL I antered (so if I enter router.mydomain.com I get www.router.mydomain.com instead, that does not exist of course). It can easily be corrected by adding explicitly http:// or https:// in URL, but it makes things less comfortable to use. Strangely, when I switch from Safari (I’m on Mac) to Chrome or Edge, everything works as expected. Also, as far as I can diagnose from home, remote access, while accessing from Internet no such problems are observed. Anyone faced similar issue and know how to remediate? Since it is happening for few selected devices only I’d blame these for… but how? Could be that this issue existed earlier, but since I was accessing RP from proviced router via NAT loopback, it was treated as access from internet and did not materialized…