A couple of clarifying questions:
How big is your house?Is the router in the corner of the building?
Is the router in the corner of the building?
Are the internal walls plasterboard or brick?
Wi-Fi signals get weaker going through walls and also the further a device is from the base station. You'd normally expect to get a reasonable signal if it travels through one wall, but maybe not so great through two. It might be worth calling BT to discuss.
My home network uses a router at the edge of the house, like a HomeHub 6, with WiFi disabled. I then have a Wi-Fi router acting as an Access Point (also called wireless bridge) in the centre of the house. They are connected using HomePlug AV. I have determined a good position for the Wi-Fi router with the help of a Wi-Fi analyzer app on my phone which let me walk around the house and check a good signal can be found all over. There are plenty of apps for this, I use WiFi Analyzer on Android.
Pretty much any WiFi router you buy will support running in access point mode. Just check the manual before you purchase. You can find the manual on the vendors website. And also turn off Wi-Fi on your BT router so there's just one Wi-Fi router competing for wireless bandwidth in your home. For most UK homes, this works fine as the properties are not too large.
The more modern approach is to go with a Mesh Network solution. These work well, but typically cost more. BT has a solution for this, so does Google, Netgear, and others. There are some reviews here:
I don't have any experience with WiFi repeaters and mini-hotspots, but I'd generally avoid having multiple wireless networks in my home to avoid additional interference and issues with connecting. You have apple devices which generally connect quickly when moving between wireless networks so this may be less of an issue.
It sounds like your home may be quite challenging. The range you are seeing seems particularly poor. I would ignore the ad, there are limits on WiFi signal strength and variations in manufacturing.
The physics are such that 5GHz has less range than 2.4GHz. For short distances, it usually offers higher bandwidth. The 2.4GHz bands is quite crowded and lower bandwidth. In the absence of competing sources either can provide good enough bandwidth for a typical home.
If the existing repeaters worked okay, I'd see if there's a way to get them to work with the new smart hub. Are there any obvious challenges with this? If the 5GHz has a different SSID or is turned off it should avoid the issues you mentioned.
Of the two options I outlined, it'd seem that going with a mesh solution might be better given the walls and range. The nice thing about mesh routers is that you can start with just two units and add more if required. There should be fewer issues with network hand-offs with mesh than having multiple wireless networks (repeaters, access points). The major downside is price.