When did you last repaste your GPU? it is a good practice to clean and repaste your CPU/GPU regularly (once a year or so).

You definitely want an 8th gen (Intel) or better to have Jellyfin Quick Sync support. It’s what I have (i5-8400T) and it offer a fairly decent AVC (h264) and HEVC (h265) transcoding for my usage. However, for futur proofing consider an 11th gen for the AV1 support.