I agree to prohibit HEX value pasting in CMYK mode to avoid misunderstandings.
As you suggested, I am currently transferring colors between documents by creating new rectangles. If necessary, I will create a new request.
Thank you, Egor Chistyakov!

I understand why you do what you do — to quickly transfer one color from one document to another.
And even though copying HEX value seems las a fast route, it kills the ink values, twice. I actually voted against of allowing to paste the values into this filed if aa color is CMYK, to avoid situations like this, but the team decided to always have it editable.

For now, just don’t use RGB handle to handle CMYK colors, this will reconvert them.

The simplest method I can offer to transfer a single color is to just create a rectangle, fill it with the color, copy and paste it into another document :)
If you have many of these, already saved as swatches, you can import swatches form one document into another.
There are other methods as well, but not a single one that will copy and paste info for all 4 ink channels — no context menu, no dedicated command.

If you wish, you can make a separate request. Perhaps other users will find it useful!
Don’t worry about translation too much, I can always correct it.

Thank you. You explained it very clearly, I understand the working principle of CMYK and RGB color modes. I think copying between different documents in the same color mode will result in the same outcome, but in reality, it is not the same.
When I tried to copy colors from one document in CMYK mode to another, I encountered this incorrect value. If I could copy it, I wouldn't have to re-enter the same color values in another document. Although creating a new color palette can solve the problem, it is not necessary to create a new palette as a temporary color.
I hope there is a quick way to copy CMYK color values instead of manually entering them.
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(The above may contain inaccurate vocabulary through software translation, please understand)

Another explanation.
'CMYK color' is just an ink formula, which CAN look like a color on your display, because an app tries to simulate these inks.
It’s not a color definition, but a 'recipe on how to cook it'.

So we have one simulation to display CMYK as RGB on display, based on your monitor’s parameters, and another simulation tries to convert your RGB HEX into ink formula, using parameters of averaged inks and averaged media they are expected to get printed on.

These two simulations differ :)

Color management is the method apps use to convert colors from one color space to another.
Here is a general help article on it: https://helpx.adobe.com/photoshop/using/understanding-color-management.html (this one is for Photoshop, since the one for Illustrator covers it differently: https://helpx.adobe.com/illustrator/using/printing-color-management.html)

This is a common discovery, and comes up over and over and over again in many places:
— https://community.adobe.com/t5/illustrator-discussions/cmyk-input-gives-different-rgb-while-rgb-gives-right-cmyk/td-p/10643146
— https://forum.affinity.serif.com/index.php?/topic/93602-cmyk-values-dont-match-rgb-values/
— https://www.reddit.com/r/AdobeIllustrator/comments/17vpbod/different_cmyk_values_for_same_hex_code_which/
— https://graphicdesign.stackexchange.com/questions/55452/cmyk-color-related-to-rgb-hex-different-online-than-in-adobe
...for every app that uses CMYK.

Explanations differ a bit, but the core idea remains the same — there are many ways to produce the same exact looking color in CMYK, using source RGB or Lab values when converting it to an ink combination. The exact mixture is driven by formulas used by color conversion engines, using different mapping intents, and are defined in Edit > Color Settings dialog (each Adobe app has one).

Color management systems allow to set these differences in a way the color you see on screen (not by RGB or CMYK values, but by actual eye perception) would match the one you get when printed — if everything is profiled, including your screen, your printer, inks and paper (since different papers and other materials behave differently with different inks).

What you do is forcing a color to be converted twice.
1. When you get a HEX value in a CMYK (!) doc, this RGB HEX value is a result of one conversion
2. Then, when you use an RGB HEX values again, these get converted to a CMY color again, as the current profile dictates
And these two conversions are NOT symmetrical and won’t be ever, since the printing profile and the profile for your screen have different intents and, well, just completely different physical ways they produce color.

Not sure it became any more clearer :)

Welcome to color management and printing, where one and the same RGB color can be presented with many variations of color inks in CMYK. Won’t be fixed ever, and it works the same across all apps which allow CMYK.

Sorry, I didn't understand the above paragraph clearly.