Front squats are a better exercise for quads.
Back squats are for your posterior chain.
You should be warming and activating your glutes before back squats.
The whole don't squat low to save your knees is a phallacy. There is less tension on your quadriceps and patella tendons on a low squat.
If you can't squat low, it's your hips that are the issue.
Are your hip flexors tight? Are you pushing your knees apart to keep your glutes activated?,
Check your feet position. Slightly wider than hip width. Slightly pointed out. Will allow a deeper squat because the hips won't impinge.
I use to be able to front squat the same as my back squat. Using a proper front rack, not crossed arms. But I have fixed the immobility and non activity of my glutes. Now the back squat has gone up again.
In the end, it's what works for you. If it was me, I would rip the plates off the bar and start again.
Activate your glutes with some x-walks and glute bridge holds. Mobilise with a lacrosse ball. Check your position and do 5 sets of 5. Each session, add 5kg to each side. Do squats 3 times a week.