With the introduction of Lightroom version 10.1 there is a known bug in the Adobe software that prevented the export of 3D LUTs from Lightroom to Photoshop. A workaround as been found while the issue is addressed.
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3D LUTs are similar to presets or color actions, except they are introduced as the first step in post-processing during the raw phase of image correction. 3D LUTs are inserted into the raw image in an adjustable format giving users the ability to infuse color prior to starting the normal post-processing workflow. To learn more about 3D LUTs navigate to here: What Versions Of Lightroom And Camera RAW Will The 3D LUTS Work With?

With the release of Lightroom (V10.1), some users report that when moving files with one of the 3D LUT profiles being used from Lightroom to Adobe, the 3D LUTs from PRO EDU are no longer applied to the image when the file arrives in Photoshop.

PRO EDU has found that when in Lightroom, instead of using right-click>edit in, if you use right-click>export>export and use the settings in the screenshot below, the LUT settings will stay applied to the overall image.

This is an unresolved bug. The only workaround is to Export or open as a smart object and apply the profile in ACR or use the above method.

Here's the forum post in Adobe's community about it: https://feedback.photoshop.com/conversations/lightroom-classic/lightroom-classic-10-color-profile-not-embedded-in-exporting-to-photoshop-v22/5f95561249d3ca123123e900