It's been a minute since I ran ZeroTier, so my memory is fuzzy.
Tailscale and ZT are not the same. ZT can do certain things that TS can't. One example is acting as a layer 2 bridge. Or a layer 3 bridge. TS can do neither. It can achieve mostly similar results though.
ZT can be a pain to setup. TS is a breeze. ZT's raw performance is quite poor. TS's is usually very good.
If I understood you correctly, you want both a way to access your home LAN when you're out - this is easy. Set up a node with NICs on the LAN subnets you want access to (I run it on my router), and configure the TS node to announce routes to those subnets. Install the TS client on your laptop and mobile and accept those routes. Job done.
If you also want to mask your egress - i.e. reach the Internet via your home network as if you were there - then you need a node (can be the same as above) configured to act as an Exit Node. When you want one of your devices to use this, just select the appropriate exit node. Job done.
Tailscale and ZT are not the same. ZT can do certain things that TS can't. One example is acting as a layer 2 bridge. Or a layer 3 bridge. TS can do neither. It can achieve mostly similar results though.
ZT can be a pain to setup. TS is a breeze. ZT's raw performance is quite poor. TS's is usually very good.
If I understood you correctly, you want both a way to access your home LAN when you're out - this is easy. Set up a node with NICs on the LAN subnets you want access to (I run it on my router), and configure the TS node to announce routes to those subnets. Install the TS client on your laptop and mobile and accept those routes. Job done.
If you also want to mask your egress - i.e. reach the Internet via your home network as if you were there - then you need a node (can be the same as above) configured to act as an Exit Node. When you want one of your devices to use this, just select the appropriate exit node. Job done.