We have done all he hikes you list, although we hiked the whole way from Schynige Platte to First instead of looping back to Schynige Platte. That is an ambitious list to accomplish in the timeframe you mentioned in your other post—-9 am on Monday until 2 pm on Wednesday, considering the travel time from Muerren as well as the hike itself. Maennlichen is the least interesting, in my opinion, so if you need to drop one I suggest it is that one. It was a nice walk to do with my 6-year-old grandchildren when we took them to Switzerland in 2018, but it is very crowded and just not as compelling as the others.
As for Oeschinensee, it is always hard for me to judge whether something is “worth it” to some else. We include an overnight stay of 1-3 nights at Oeschinensee in the Berghotel by the lake in almost every visit to Switzerland. Our favorite hike there is up to the Fruendenhutte alpine hut above the lake. The trail ascends the cliff that arises from the lake by means of ledges, and is truly spectacular—-and a unique experience. The ledges are wide and stable and provide good footing, and there is a steel cable against the rock to grip if one is nervous.
https://www.fruendenhuette.com/
The panorama trail you mention makes a loop above the lake in the other direction. I have hiked one of those trails on the way to Blumlisalp Hutte on the other side of the lake from the Fruendenhutte, but not sure if it is that one, so I really cannot comment. We do like the lake-level “sculpture path” but that is just an afternoon stroll, sometimes linked with a swim in the (cold) lake.
But when would you go to Oeschinensee? After you leave Muerren, on your way to your next destination?