MBP won't use 5ghz

What model and how old is your TC?

In normal setup the TC will use same SSID (wireless name) for both 2.4ghz and 5ghz.

Sometimes in order to force a computer to use 5ghz use a different wireless name. You can do this via wireless options.

I do recommend you reset the TC to factory and start over with fresh configuration. No files are lost on the hard disk. You will need to redirect Time Machine to the renamed TC but that is simple to do.

Use short names with no spaces and pure alphanumerics. e.g. TCgen5 and wireless names like TC24 and TC5

Passwords same rules but longer 8-20 characters. This is important with Catalina which uses very different configuration compared to previous OS versions.

Wireless can deteriorate in the TC.. hence one reason why your laptop may not work on 5ghz and the wife's MBA is not managing to connect to 2.4ghz.

I recommend download and install a simple wireless analyser like netspot but you can also use the built in diagnostics.

Here is a screenshot from both of them.

Also hold down option key and click the wireless fan in your Mac to get more data.

You can also see signal level at the airport from each of your Macs. Place the cursor over the wireless clients.. listed by name, IP or MAC address. A popup will appear with helpful info on signal level like RSSI etc.

Compare signal levels in the same room and then from next room and then one after that. Look at my signal levels.. if you want high speed you need really high signal. Remember signal RSSI is a negative number so -30dBm is a lot more than -40dBm .. signals below about -55dBm will give poor results.. and -70dB is dropout point with hugely unreliable operation.

The TC is 5 years old and I believe it's the A1470

Thanks for the update and all the extra info.

Yes, that model number corresponds to the age. It is fairly old and wireless is one of the first things affected by age.

Simple fact is you need a new router. You can keep the TC as a backup target only until it finally bites the dust.. but you might want to reconsider the whole thing.

I never saw a way to create 2 different networks (one for 5 and one for 2.4). Is that possible with the TC and/or recommended?

As mentioned it is under wireless options.. but you cannot do it during setup. The setup wizard is very basic.

So click on the icon of the TC in airport utility.. click on edit in the summary that comes up.

Now you can alter the configuration of the TC.. click on the wireless tab. Note near the bottom Wireless Options.

So in here you name the 5ghz to a different name.

This looks like a rather old screenshot so perhaps you will not see Radio Mode..

Now this is recommended when you have issues like you are experiencing as you can then control how the wireless is used by the client. It takes more effort but in my experience helps.. BUT others will say equally valid that it is best left to the Airport and client to negotiate the band used. As you can see in your case this is not working.

Couple of things.. Check if you are using Norton AV or any third party security software, speedup cleanup etc adware.. remove all of them.. This is especially important for Catalina.

Is the issue on the laptop side.. remember your laptops are also getting older and wireless cards in the Mac are known to give trouble. I think that might be the case in your situation where your laptop is making such poor speed.

Have you upgraded several times over the years without a clean install of OS?

As horrific a prospect as it might seem I think a clean install of OS is well worth it.

You do not need to ruin your current setup.. just use a small USB SSD plugged into the laptop and you can set that as a boot drive and use it for clean install. If that fixes things then transfer that install to laptop built in drive. You will also migrate the current files and apps.

If it was me.. I would get.. borrow or buy from store with good return policy a new router and see if the problems go away. If so then TC was clearly the issue.