To add to other comments, consider a managed switch from MikroTik. Linux networking knowledge will come in handy, since their RouterOS is not especially simple but it is powerful.
I believe most of their devices jump from Gigabit ethernet to 10Gbps SFP+ ports (which you should also consider). The SFP+ ports usually support 2.5Gbps negotiation, but check the documentation. You can also buy RJ-45 Copper transceivers for the SFP+ port, although they are not cheap. Nevertheless, even including a couple transceivers, you may find something within your budget.
Using a router-on-a-stick configuration, consider a CRS305 (4x 10G ports and 1x Gigabit port) or a CRS309 (8x 10G ports and 1x Gigabit port) switch.
As for their routers, multi-port-multi-gig options are expensive so building your own router might be a good idea rather than opting for something like an RB5009, if that is what you need. Although, in a router-on-a-stick configuration, an RB5009 would be great.
Wi-Fi: yes, you can connect an access point to any ethernet port from a router or switch. They often come with PoE injectors.
Consider TP-Link Omada access points. If you need multiple access points, they suggest running a controller, it can be installed as a docker container. MikroTik has access point options but my experience with their old wireless options left a bad taste in my mouth. I hear the new wifi-wave compatible hardware is good, though. Any device running RouterOS could act as the CAPsMAN (AP controller)
Signal does have group chats, and has had them for at least 10 years.