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.

Jokes aside, from what age is it recommended to check your balls annually as (for early detection/prevention of prostate diseases)?

Finally, something that does nor relate to US election. But, WTF did I just read?!!

For Jellyfin, dont get any lower than 8th gen if you want to transcod using quick sync. And if i correctly remember, you will nee 10th gen or higher for 10bit transcoding.