Dear Misaki:
The following is the error content:

Spine Launcher 4.0.34
Esoteric Software LLC (C) 2013-2021 | http://esotericsoftware.com
Windows 10 Enterprise LTSC 2019 amd64 10.0
NVIDIA Corporation, NVIDIA GeForce GTX 1050 Ti/PCIe/SSE2, 4.6.0 NVIDIA 516.94
ERROR: An error occurred starting 4.0.61: C:\Users\Administrator\Spine\updates\4.0.61
[error] Error validating update file.
at s.pzG.(:995)
at s.pzG.(:490)
at s.FAJ.S(:42)
at s.FAJ.
(:32)
at s.wJO.
(:65)
at s.IWk.
(:98)
at s.xRn.
(:47)
at s.MIy.
(:226)
at s.EWR.F(
:604)
at s.Lpt7.run(:262)
<events>
Cause: [error] [0x05]
at s.pzG.
(:985) ...
Downloading: Spine 4.0.61 Professional
ERROR: The update file could not be written. Is it in use?
[error] Unable to write to update file path: C:/Users/Administrator/Spine/updates/4.0.61
at s.pzG.F(
:351)
at s.pzG.S(_:316)
at java.util.concurrent.ThreadPoolExecutor.runWorker(Unknown Source)
at java.util.concurrent.ThreadPoolExecutor$Worker.run(Unknown Source)
at java.lang.Thread.run(Unknown Source)

Related Discussions
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The error shows that for some reason Spine is unable to download the update file because it can't write the update file. Please try rebooting, in case some other software is preventing the update file from being written.

Also your Spine launcher is version 4.0.34. Please try downloading the latest Spine installer from your Spine license page and reinstalling. This will give you the latest version which is 4.1.12 and that may work better.