You should first consider replacing that narrow drain with something wider than can handle the amount of water you are experiencing.

NDS is a brand that offers wider drains.

The gap between the drain and the foundation , can be filled Deck-O-Seal from W.R. Meadows. Prior to it's application, the gap can filled a foam backer rod or can be filled sand to allow support of the sealant.

We use this around a pool between the back of the coping and patio. Not for pavers though. We install mostly natural stone patios.

Thanks so much, the Deck-O-Seal product looks like exactly what I need. I would LOVE to replace this with a wider drain, but it's thousands of dollars due to the size of our patio. Hoping someday I can rid myself of these high maintenance pavers, get a nice wide drain & natural stone or outdoor porcelain :)

You are welcome. The Deck-O-Seal is the best stuff. Been using using for decades.

It's a 2 part mix so follow the instructions explicitly.

There are color choices. We use Gray the most.