It sounds like you may be confusing how Zigbee works with how older WiFi works.
In WiFi you would have a single access point with a certain range. If you want to extend that range in a particular direction you would have to add a range extender, creating a chain or rope of range extenders.
Zigbee (and many modern WiFi APs) are more like a fishing net. The more relays you have the stronger your net is because if one relay goes down for whatever reason, another relay in range can pass along the message to where it need to go.
By the by, this is also how the internet works (oversimplified to the point of inaccuracy of course).
In building out a Zigbee network you do not want to create chains with a single path available for reliability reasons. It’s better saturate an area with Zigbee relays. The relays can be either bunched up or you can spread them out. The only limiting factor on the size (in sq meters) is the max number of devices of the protocol, which you are unlikely to hit, and the radio range of the individual relays. Each device (either a relay or end device) needs to be able to see at least one (but preferably more than one) relay.
At a high level (I don’t run one myself), A Zigbee to MQTT server is a way to create a second “net” that is completely separate from the your original Zigbee network. In a nutshell, you take a second Zigbee cordinator and attach it to a MQTT server which then passes the information back to your Home Assistant. This second network doesn’t benefit from the first and the first doesn’t benefit from the second. Though, because they operate on the same frequency spectrum, they can conflict just as 2.4Ghz WiFi and Zigbee can conflict.
Can I just get a zigbee to MQTT router and that bridges between a zigbee button and HA?
It’s more something that you build than something you get, but, practically speaking, there is nothing stopping you from doing so. Though it doesn’t usually make sense to do so from an effort or infrastructure prospective for a single end device. Though of course, there are always exceptions. At a minimum, you would need a network connected computer running the MQTT server and a second Zigbee coordinator. Search for zigbee2mqtt.