I was the lead engineer on a mesh wifi system. Not only do I recommend mesh WiFi, but I high recommend you throw your extender in the garbage. Many extenders cause wireless interference, which will actually make your quality of connection worse on both networks. They are essentially a second WiFi network in your house. Some smart ones will put you on the same subnet so your devices can communicate with each other across networks, but the router and extender will not tell your device when to switch from one network to the other. This will mean that whichever one your phone connects to first, it will stubbornly stay on until you either turn your wifi off and back on on your phone, or your phone's wifi connection is so horrible that it can't communicate at all. This is what mesh does well. It sends a message to your phone saying which node you have the strongest reception to, and assuming your device supports mesh AP steering (most phones made in the past decade do), your phone will automatically hop to the node with the strongest signal as you walk around your house.

The price of mesh networks has come down dramatically since it first got popular a decade or so ago. Ideally, you could have a wired connection between nodes, but it isn't required. You just may need more nodes to make sure they all have a strong connection with each other. Remember that mesh nodes are going to have much larger antennas than your cell phone or laptop, so they will be able to get decent reception in a spot that your phone might get just okay reception.

Invest in a mesh WiFi network.

They can be pricey but perfect for old buildings with thick brick walls.

https://www.techradar.com/news/best-wireless-mesh-routers

If the power lines are good, you can fairly easily extend your network with ethernet over powerline adapters:

https://www.amazon.com/NETGEAR-Powerline-Adapter-Ethernet-Passthrough/dp/B0778Y6K6N

You plug one unit into an outlet close to your router and connect it to your router with an ethernet cable. You plug the other unit in in any other room in your house and connect it with ethernet to a computer, a second router, or any other device that has an ethernet port.

You can buy flat Ethernet cables, you may be able to run a few of them under carpets, along the walls, etc. and install access points in several rooms.

If the building allows that, this should be the best solution. If not, you're stuck with meshes.

Wireless-only mesh is only as good as the weakest connection. You want mesh routers connected via ethernet or powerline where possible.

I've seen people run ethernet over rooftops and outside windows around houses.

In terms of performance, the best option is multiple wired together access points. You can get flat Ethernet cable that can easily fit under doors, carpets and through windows if you don't want to/can't drill any holes in your walls. Mesh networks are an option, because the mesh nodes generally have higher power transmitters then your device, but this will be slower then a proper setup, and get slower the further you are from a node with a wired connection.

If you are on 5 GHz, try moving to 2.4 GHz, the top speed is slower, but it much better at passing through walls.

You could look into MOCA adapters if the house has existing coaxial cable installed through walls for an old cable TV system. Plug an extra access point or two in and connect back to your main router via a few sets of adapters. It can cost a bit up front but it’s pretty reliable and if you buy old used 2.0 models you can save some money. (Just make sure they’re the same manufacturer)

Otherwise your options would be power line adapters to access points (bad, lots of chance for interference, neighbors adding a heavy appliance could break it).

Or nicer extending units located more closely together though if your walls are masonry or brick that may not help.

Also, inelegant and I hate to mention it but you could buy long, flat Ethernet cables, run them along the baseboards with the special retaining staples and connect that way to access points, though it does require space of a few cm door clearance in every doorway it has to traverse. Also flat cables technically violate Ethernet spec for preventing interference but in most single family homes interfere isn’t a big issue away from power supplies and runs so it would probably be okayish.

Echoing everyone here, I have a mesh setup in my house with thick plaster and lathe walls, and it's good enough.

Problem areas:
Outside. We have aluminum siding, and it helps and hinders. Signals outside the house can't really get in at high strength, so the Wi-Fi frequency range is clear. Same problem though, I don't get signal in my backyard. This was fixed by putting an access point near a window.

My first floor ceiling is metal. (Looks like copper underneath the paint). Signal doesn't want to go upstairs. Solved by putting access points near the stairwell both up and down.

A mesh has others have said. I use Google WiFi as it's cheaper and gets the job done. But it's a potential compromise as the more expensive mesh systems offer better bandwidth.

I tried Homeplug systems - they can work well on a well wired house, but mine was giving me about 10% of my bandwidth from the router downstairs to my home office upstairs.

For comparison Google WiFi is giving me 100% of my 250mbs connection. If you're looking at much higher bandwidths or users, you may need a more expensive system. Alot of mesh systems have a dedicated back channel separate to the user facing channels but Google WiFi does not - that makes it cheaper but could be a bottleneck if you you're at the very high ends of internet speeds and home usage. For most home users though I suspect Google WiFi is more than enough.

Mesh is terrible, don't fall for it. It can get you at least some connectivity in the extended areas but it won't be good connectivity.

The only actually good way to extend WiFi is to install access points and run cables to them.

Cables don't necessarily need to be regular ethernet but that's usually the best option. MOCA usually also works great. Powerline can be hit or miss, I'd only consider it a last resort and even then wouldn't expect it to work well.

Get a WiFi Repeater. They do exactly what you want and are not expensive. When I used to live with my parents, I had a room in the basement with no connection. I bought a repeater for 30€, plugged it into a near socket that could catch a signal from above and the problem was solved.