Guidance to replace my raspberry pi 4

[Host-in-the-Shell]

Considering SBCs are not recommended, which includes Raspberry Pis, I think anything that exceeds their computational power will be a significant improvement.

For a server without a GPU, here are the recommended specs:

• CPU: Intel Core i3-7100, Apple M series or newer (excluding Intel J/M/N/Y series up to 11th gen)
  
• RAM: 8GB System RAM (Consider adding more on Windows 11)
  
• Graphics: Intel HD 630, Apple M series or newer
  

I'm assuming the 120GB SSD will be used as a host for the OS. If you don't plan on transcoding multiple streams often then there's no issue; otherwise you probably could use a larger SSD; if you can make it an NVMe, which the Fujitsu D538 seems to support, even better. While storing transcoded files in the HDD is possible, a faster disk is better.

Optional: If you're not on a tight budget, I'd take a look at a mini pc with a 12th gen N100; it may cost around 50€ more, give or take, but it would be a significant upgrade with much better hardware, with low power that could cut costs in the long run, and it would even handle transcoding very well for a media server. The tradeoff is that you won't have the 1TB HDD and you can't really fit one of those inside, but you could later invest on an external disk to attach to it.

All that said, since your goal is mostly to direct play, your current specs are totally fine.