There may very well be a “rainbow bridge”. Anything is possible. It’s a nice thing to believe in – a very positive thing.
Ultimately, it’s up to God as to whether or not we are reunited with our departed pets, and whatever God decides, it will be right, even if He says no, and we will be okay with that. Because, we know we can trust God, as He is perfect, and perfectly righteous.
Grieving for a lost pet is no different than grieving for any close friend who has loved you unconditionally, and has enriched your life immensely. It’s normal.
You have given this kitty a wonderful life during the time he had left… By adopting him, you actually saved his life. It was kind of you to adopt him, and it sounds like he appreciated it, and returned the favor with a great deal of affection.
Some say that animals (including pets) are for earth only, and have no afterlife. We don’t know that. There’s a Psalm that seems to declare otherwise – a Psalm that tells us God will preserve the animals. That can be interpreted to mean He preserves the animals while they’re here on earth, or it could mean He preserves them for all of eternity.
I personally believe that love is eternal, and cannot be extinguished.