Help with Adguard DNS on NAS

Tailscale version : Latest
Your operating system & version : Synology DSM 7 and Windows 10

Basically I have the Synology DSM 7 running Windows 10 VM (and I have Adguard Home running on VM)

Now my ISP has CGNAT(double NAT), so I came across TailScale, and this has been great.

But I was wondering if I can use the Local IPs remotely rather than using TailScale’s IP, so I tried to Advertise Subnets. And it works, my local IPs became accessible remotely, but my Internet went down in my Local Network (Home), due to DNS issue.

So if I want to get the internet back running on my LAN, I either have to turn off the Advertised subnets or I have to use the Free DNS resolvers available and not the Adguard’s Home DNS address.

What is the solution here, if I want to keep Internet running at my Home with Adguard and also access the local IPs?

Any help would be great. Thank you, and sorry if this questions was stupid, as this is my first time with Home Servers.