Did it really make him look weak, though? He's consolidated the military under the MoD umbrella, his comradery with Lukashenko likely improved, the West is admitting that Ukraine is running out of ammo (thus the cluster ammunition) and he (or rather Lukashenko) has a strong private army close to the Ukrainian border, about 90km from Kiev.

The only people claiming his weakness were some Western officials and the press and both haven't been particularly trustworthy nor well informed in their assessments of the situation thus far.

Edit: Not to forget that Prigozhin made it clear that his problems weren't with Putin but with MoD leadership/Shoigu.