First time travel to Japan/Korea : 20 nights 6 cities

My partner and I are planning a December 2026 trip to Japan and Korea. it’s a pretty big milestone trip for us and we want to make sure we’re planning it right before booking local flights and activities. We’re planning 20 nights across 6 cities:
1. Tokyo: 5 nights
2. Seoul: 4 nights
3. Busan: 2 nights
4. Kyoto: 3 nights
5. Osaka: 3 nights
6. Tokyo: 3 nights (back for Christmas)
We’re flying in and out of Tokyo and doing Korea in the middle before returning to Japan for Christmas. December is totally intentional btw.
A few things I’m unsure about:
Is it really worth it to go to Korea for a week in between (we’re thinking it’s 2 for the price of one)
Is 2 nights enough for Busan?
Should we stay in Kyoto (3 nights) or base in Osaka and do Kyoto as day trips
Anything we’re missing or would you restructure anything?

Appreciate any advice thanks