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Hi Rastislav Janotka,
I went through your post carefully and do understand your great idea of trying to update the custom field without triggering a version increment.
In this situation, I also searched online and from what I found there may indeed require the REST API with specific headers and body parameters to call, so to make sure you can get the professional and appropriate support from SharePoint escalated engineers, I recommend you post in the related Microsoft Q&A Community, which is the specific channel to handle such SharePoint developed customization and engineers there have more overall support resources like REST API. You may use SharePoint Development tag when" Ask a question".
Please accept my apologies for redirecting you to different community as the members in the category posted focus on the users with out-of-the-box functions and quires on SharePoint Online, and have limited knowledge and resources on the development customization, so to get the fast and better assistance, we have redirected you in the correct path.
Meanwhile, I will keep your thread open here and welcome other community members or MVPs may share their suggestions and experience for you.
Please correct me if I made any misunderstanding or if there have anything else I can do for you.
Your patience is highly appreciated. Hope you a nice day and stay safe!
Best Regards,
Mia