Worth, of course is something only YOU can determine.
Gaming(excepting multiplayer) will only use a handful of threads perhaps 6.
Performance depends mostly on the performance of the single master thread.
Your current I5-4690K has 4 threads and a passmark rating of 5575. That is when all 4 threads are fully busy.
The single thread rating is 2188. Arguably the more important factor for gaming.
The proposed $158 I5-12400f has 12 threads and a rating if 19538/3531. A very nice bump.
Thinking about it, have you considered the $117 I3-13100?
It has 8 threads, but a passmark rating of 15611/3767 which should be comparable performance for games.
As a plus, you get integrated graphics This is valuable insurance in case you should ever have discrete graphics card issues.
And... fwiw, the 3600X which Math-Geek was so happy with had a lesser single thread passmark rating of 2673
Two other thoughts:
As perhaps a better ssd setup, look for a single 2tb m.2 ssd.
Do not chase faster sequential specs; you can not tell the difference.
What is the make/model of your current psu?
It will be fine for now, but your future gpu upgrades may be limited if the psu is not sufficiently strong.