Oh @JaceLancs I didn't know you had lost lovely Finlay - I am so sorry.
Everyone is different, but here is my experience. We lost our lovely girl to intestinal lymphoma in April 2024 and it was all a terrible shock. We'd had her back and forth to the vet for vomiting for months but they were never concerned because otherwise she was fine, until I pushed for a referral out of the surgery and they found a massive tumour. (No shade on our vet, even the specialist vet said she expected it was IBD when DP dropped her off for the scans.) We let her go the following week and while it was the right thing for her, it broke our hearts.
I saw Louie on the Cats Protection website a few days later and just knew he was meant to be ours, but I didn't expect it to all move so quickly, and within a week he was home. My DP was away for work and came back to a new cat. I can remember a few weeks after that my friend who came with me to the foster carer to meet him being round for dinner and saying, "do you love him?" and I was actually shocked. I said, "no, he's the wrong cat, but I hope I will in time". Now we're two and a half years on, and I love him wildly - he's such a different cat, and I am sure my girl sent him to me as a wee project while I was so, so sad. I'm teary just writing this because I still miss her so very much! Louie didn't replace her in any way, no cat could, but he gave me someone to love at a time when I needed it - and he was a little lost boy who had been a stray kitten living in a woman's shed and needed someone to love him.
(As balance he's a total bloody pest a lot of the time, mind.)