Hi Shikabashi,
i have the same problem when i try to export it as webm or mov-file. In editor it is fine: i compared the first and last frame and both are the same, but when i export it and the animation begins from start there is a small difference as in your bone-animation to see. Nate has written something in spine-discord:

"that could be done in the export settings using Animation repeat and Frames: Range to cut out the looping part. the pain is finding the frame range to use"

I tried it and in export-preview i could see no difference (compared first and last frame), but when the file was exported, there was a visable small "jump". Hope we can find a solution.

One of the benefits of physics is that your animations don't look repetitive. Physics works great for loops using a runtime, but physics behavior is inherently dynamic and doesn't lend itself well to perfect loops in exported images or video.

If you must have perfect looping in image or video exports, I would suggest to not use physics. Otherwise the only solution is as described above: export the animation repeating 3+ times, then cut out the part that loops. Even then it may be difficult to get it to loop perfectly.

Nate Can unity runtime use real-time spine physics simulation?

All runtimes will be able to use physics constraints. It was just release in the editor as a beta. Currently only spine-libgdx supports physics. The other runtimes will support it soon.

Nate Sorry, I didn't express it clearly. What I meant was whether the unity runtime can calculate physical effects in real time like in spine.

Yes, all runtimes will compute physics constraints dynamically, just like they are computed in the Spine editor. This gives you dynamic movement from physics across animations. You can even have movement in the game world affect the physics in your Spine skeleton.

Nate Does it have a big impact on performance?

It is efficient, similar to other constraints. It shouldn't be a performance problem in most cases.