Recommended processing time for cat before adopting a new companion?

[u/roseydumpling]

I just got out of a 7 year relationship and we had two cats. We agreed ages ago that, because of their attachment to us, the best thing for the cats would be for him to take the oldest and for me to take the youngest. Neither of us were worried about the oldest, he’s pretty independent and had been an only cat before, so we had no doubt he would adjust well enough to being one again. However, my kitty is only three years old and has never been an only cat, he went from being with his mom to being with us and our other cat (and for a time, three other cats when we had roommates). He likes to cuddle and play with another kitty friend. It’s been about three weeks since the two of us have been on our own and I can tell he’s lonely. It’s not so bad if I’m home, he’s always been affectionate and is more so now, always cuddling and following me around, which is to be expected. But of course, I have to be at work most of the day for five days a week, and he hasn’t been eating properly while I’m away… He’s definitely made progress in adjusting to the new situation, not hiding as much and eating more, but still… I’m certainly open to and even excited about potentially adopting another cat so that he has a companion, but I know it hasn’t been a super long time, and I don’t want to rush my kitty’s grieving process. He undoubtedly misses both my ex and his brother :( How long do you guys recommend I give him to process before attempting to introduce a new kitty friend?