.RU is somewhat complicated, as the domain ownership is a separate thing. Paperwork may be needed to change the domain ownership, or to confirm the ownership with your new registrar. Tecnically, there are authcodes for transfers. See, for example
https://www.nic.ru/help/domain-transfer-to-ru-center-from-another-registrar_5746.html :
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Domain transfer to RU-CENTER from another registrar
For .РФ, .RU (a paid service):
get a transfer code from the current registrar;
submit a request for registrar change in the «Manage your account» section → Domain transfer;
confirm the transfer.
The e-mail of the domain administrator specified for the domain of the current registrar will be sent an email with a link to confirm the transfer.
Registrar change procedure cannot be performed in any of the following cases:
less then 3 days before the end of the registration period;
identification procedure is not passed;
judicial or pre-trial restraints are established regarding the domain name;
the domain administrator did not provide additional information at the request of RU-CENTER in the specified time;
less than 30 days passed since the last ownership change;
less than 30 days passed since the last registrar change.
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So, you should simply follow the instructions of the gaining registrar or reseller.
Warning: if you are not located in Russia, you may have difficulties with .RU domains at this time. A number of non-Russia based registrars or resellers stopped doing business (new domains/transfers or any domains/transfers) with .ru domains due to sanctions. While you may always select Russia-based registrar for your .ru, you may not be able to find a way to pay them, as international credit cards and paypal are not working in Russia at this time. Some russian companies are still able to accept the payments from abroad using third party billing solutions though.
Official registry website (rules and full list of accredited registrars):
https://cctld.ru/en/domains/reg/
