Update non-steam-playtimes to v1.2.1

[k0d13]

non-steam-playtimes

Fix playtimes not appearing after using Big Picture mode
Fix playtimes not being tracked in Steam beta
Add better protections for the sessions.json file

Task Checklist

Developer

• I am the original author or an authorized maintainer of this plugin.
• I have complied with all license requirements for the libraries used, including providing appropriate notices where necessary.
• My plugin is fully open source and does not depend on any external paid services, except for widely trusted and well-known platforms. Additionally, neither I nor anyone associated with me profits from any such services.

Plugin Functionality

• I have tested the plugin on both the Stable and Beta Steam update channels.

Backend Configuration

• Yes: I use a standard Millennium python backend in my plugin.
• No: I use custom binaries that or rely on other FOSS projects that aren't written directly using Millennium's python backend.

Community Contribution

• I have tested and left feedback on two other plugin pull requests.
• I have added links to those feedback comments in this PR.

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Testing Instructions

• Verified by a third party on Steam Client Stable.
• Verified by a third party on Steam Client Beta.