I'm assuming you want to keep the 650b wheelset for commuting, as otherwise you will need to buy two sets of new tires instead of one (offsetting the cheap aspect of the search). In that case, even if you could squeeze a 29r rim in you would be limited to narrower tires for it. If your goal is off road, mtbing, you want the wide option going with a 650b wheelset will allow.
A 650b x 45 has a circumference of 2117.43mm
The match for that in 29r/700c is 29 x 26
That's a very narrow road tire. You still have some room it looks like but not so much that you can fit a decent sized mtb tire in.
Here's a calculator
https://www.bikecalc.com/wheel_size_math
In the left column, look for the tire size you have now. Then go across to the far right column and see the circumference.
Now look at the rim size you want and try to match the circumference, that will show you the tire size.
Or, look at a 29r mtb tire size 2.20 is not bad. That has a circumference of 2305.18
The closest 650b tire size is 3" (2313.47).
Will your current bike fit a 3" tire?
If not, it won't fit a 29r 2.20 mtb tire either.