It is uncommon to host a web server on a mobile device. A more typical setup would be to set up the Whoogle instance on a normal computer and connect to that from your mobile device.
If you have an "always on" machine, it's pretty easy to set up a web server. If it is just Whoogle on there, a low-resource machine like a Raspberry Pi or an old laptop you don't use anymore is fine. One simple way I have done it is to set up a DDNS domain (I don't have a static IP address from my ISP), which is free from duckdns.org or similar. Then deploy a web server like Nginx or Apache and get an SSL cert through Let's Encrypt, using Certbot to obtain and renew certificates.
Whoogle also can be very easily set up in Docker, so you can get everything on one Docker Compose yml and bring it up with barely any effort. Then you can set up your website as the default search engine in your browser, etc.
If you don't want to set up a publicly accessible website, another very easy-to-set-up option is to use Tailscale and set up your Whoogle server somewhere on your Tailnet. Navigate to the Tailscale IP address in your web browser when you want to bring up Whoogle, and that's it.
Either one of those options is totally free, except for the hardware you will need to host it on, but another easy non-free option would be to set up a $5/month Linode or something like that and set up your Whoogle server on there.
The public instances are convenient because you don't need to bother setting anything up, but it really is nice having your own because it's super fast and you never get rate limited.
My always-on hardware is my rooted rugged smartphone with access point + vpn tethering, sftp+https server, adway with thirteen source lists and termux. All my devices (4) use it to connect the internet (so my smartphone provides a clean internet access). I had vpn with port forwarding (so good that my name domain point to it and replace ddns service) , but this feature will be stopped the next month (f***ing Mullvad) . So I will change vpn provider.
All this to say that it would been great to had whoogle capability to my project of nomad full featured versatile standalone server in pocket.
And incidentally, for calls and SMS. But it's rare...
I will search if it's possible to compile whoogle into termux environment. Android stay a {Linux,Unix}-like OS.
First disadvantage: my public is ip my real ip. It is not modified.
The second: I can't get my domain name to point to my vpn easily.
There are others, but to be brief, Tailscale is Wonderful for historical function of vpn with much benefits (if I have good understood), and I keeping it in mind. I am going to need it coming soon. Thank You for this.
So it's easier for me to adopt vpn service (for privacy and more) with port forwarding feature (to bypass CGNAT of gsm). It requires only 2 steps: set public ip at my registrer (DNS type A) and set port forwarding in vpn config.
With Tailscale, you do not use your public IP--even for devices directly connected to the WAN. Tailscale sets up its own subnet in the 100.xxx.xxx.xxx address range (a private or non-routable IP range). If you want to access a device on your tailnet you use the Tailscale IP.
Run tailscale status from the command line to see the IP addresses Tailscale has given your devices, or just look at them in the admin panel when you log in at tailscale.com. Or if you download the Android client, that will show what Tailscale IP each connected device has as well.
And that's just one of it's use cases. You can use another device as exit node (speak: act as full VPN), force the same DNS server on all devices (eg. for adblocking), use the Cloudflare tunnel like "funnel" service and all that strictly regulated on zero trust principles via ACLs. Needless to say, I became a big fan it lately
Oh, and sharing devices with other friends using Tailscale is also easily possible.