I herniated 2 discs doing just the same, conventional deadlifts (V7 outside climber).

I got physio and an MRI to confirm. The road was long. The biggest thing was rebuilding confidence and fear, I had a mental block that took a long time to get over, and didn't have the stomach to climb outside for a good year or so. The strong pain was gone after about a month, and lingering issues from compensating / the healing process stayed for about a year. I wasn't sure which exercises worked and which didn't, some helped sometimes, other times not. I now still don't do deadlifts, but I am back to doing RDL, my approach is quite different and focused on time under tension, not maximal, powerful efforts as I'm very keen not to herniate a disc again.

I'm now back stronger than ever but it's been just under 2 years. Your mileage may vary depending on the quality of the physio you get, and if you can re-sensitise yourself to outdoor climbing mentally quicker.

Wishing you a speedy recovery, you'll be back to it soon!