I have a proxy server running on my home server and I want to advertise it so that any client (mostly phones) can connect.
Is it possible to do so?
Transparent proxy is not an option for me.
For the HTTP proxy part this can be done via DHCP.
While you can set the proxy URL in your PAC file to point to a socks server (using the socks scheme) that's somewhat redundant if you have a working http proxy service. Things other than HTTP clients proably won't use the DHCP mechanism. There is not (currently) an option in DHCP for socks. Nor is there explicit support for it in mDNS. You could set up SRV record but I suspect none of the client applications will use this.