You are getting strong bars from a mesh satt unit because the connection to it is strong. Think of this like being right next to a cell tower and checking bars on your cell phone. You'll have a very strong signal. Now cut the cables that lets that cell tower communicate over the internet and/or to home base. You'll still have the same strong signal... but no cellular communications. If you took that mesh unit deep into the deepest desert and powered it with a battery, you'd still have a very strong wifi (bars) signal from it. But obviously, it is not connected to the internet. The bars represent strength of signal from router to device... not quality of internet signal.
Your problem is very likely the connection between it and the "mother" unit is weak or nill. If you know it will connect to the mother unit, take it closer to the main unit and then see how it does in providing internet access. Assuming that will work, you need a better way to get signal out to the garden building. My first suggestion would be to run some ethernet from main router to this unit in the garden building (this could even be buried cable). That should get internet to the mesh unit and then your strong wifi could actually connect to the internet out there. Why? Because the mesh unit is getting actual internet signals from the main router unit over that ethernet connection.
Same advice if you have a little internet (super slow). Mesh unit is probably too far or there is too much interference between it and the main unit. They need to be closer together or better connected. Since you can't move the garden building, you'll probably need to route internet signal to that building. And again, the very best way to accomplish that would be to get a wired connection between main router and this mesh unit.
If garden building and main router are relatively close together, my next guess is that the mesh unit is NOT synched up with the main unit. Read the setup instructions and be sure they are connected. The app or webpage for setting up a mesh system should show that main and satts are connected and have a good signal. I bet if you check that for yours, you'll see that the main is showing that it is NOT connected to the mesh unit or- if it is- that the signal is very weak/nill.
An easy test if the state unit has ethernet jacks is temporarily connect your Mac to it over ethernet and turn off wifi. That will completely rule out wifi out there. If you have speedy internet over ethernet out there (run a speediest), there DOES seem to be something wrong with wifi out there. However, if ethernet is also super slow-to-nill, that's absolute confirmation that the link between satt mesh unit and main router "mother" is not established or significantly strained by distance or interference.
Again, if distance is not too great, you might be able to bring the mesh unit in much closer to the main, get them connected to each other and working. And then start an experiment in which you move it 25% of the way to the garden building and seeing if you have speedy internet (run a speed test), then 50%, then 75%, etc. Bars should be consistently strong but trying to access the internet at each stage may reveal the problem (distance/interference). And if so, the best option becomes getting them "hard wired" connected with an ethernet cable.
Lastly, is garden building wall made of metal? If so, you may find you have great internet right to the wall but then it plunges on the other side of the wall. If this is a contributor, you need to get the mesh unit near a window. Imagine the signal from main to mesh as a weak laser beam and you want the laser to pass through glass instead of trying to pass through metal.
