Hi @FozzieBear,
I'm not sure I follow what you/your ISP is suggesting. They're saying that you're having problems with your broadband because you connected a 24-port Ethernet switch to your broadband modem/router? That doesn't make any sense unless the switch (or some of the cabling) is defective.
How many total network clients do you have in your home? The total of wired and wireless devices (I have about 60-70). Most people use DHCP to assign the IP addresses to their network devices. Usually, the DHCP "server" is inside the router (this device supports NAT, firewall, DNS, and DHCP services) normally. In general, it is often best to use the modem/router supplied by the ISP for "optimal" support. But some folks choose to supply their own or upgrade.
Make sure you're DHCP server/configuration is able to supply enough IP's for all of your devices. Sometimes these are set by default to 20 or 50, for example, and you may need to increase this if you have a lot of devices on your network.
In terms of connecting your TP-Link AP's to your Router/Switch. It is best to use Ethernet whenever possible. Ideally to 3 of your EAP225's. If this is not possible, then connect at least one with Ethernet and use the wireless MESH function within the Omada controller to MESH the other two to the hardwired one. You can purchase the OC-200 Omada service device (from Amazon for $86). Or you can download and run the software version for free.
The Omada management application brings a number of advanced functions 1) Fast Roaming, 2) MESH Config and failover, 3) Centralized administration, configuration, and monitoring, 4) remote cloud connectivity (for management only) if desired.
You do not need to buy a TP-Link home router. Nor will a TP-Link home router "MESH" with the EAP225 product line.
Can you describe your "broadband issues" in more detail? You state that you have FTTH (Fiber to the home). From your ONT how is your current router connected? Ethernet or Coax?
-Jonathan