My children were exactly the same - needed to sit bolt upright.
Like pp, I used a reins harness with the D rings on the pushchair seat.
I would really recommend, it is very secure, but the child still has freedom of movement. You can use the harness for high chairs in cafes too, or supermarket trollies.
And the harness is handy when walking, with or without reins clipped on.
If you look at your pushchair, there should be a solid ring at each back corner of the seat, where it meets the back, that’s the D ring.
When you buy a harness, it comes with a long strap (the reins) with clips at either end, and two short loops with clips - you attach those to the D rings by passing the end through the loop and pulling it tight, and then clip the harness on with the child already wearing it
When you get out of the pushchair you just unclip it, no need to take the harness off, so it is very quick and easy. You can clip on the reins instead when you get out, if your child is an escapee.