They already tried that with TamTam (https://tamtam.chat/) which is also owned by Mail.ru Group. I don't know anyone who uses it though and ICQ had a huge userbase in early 2000's in Russia, so maybe that's the reason?

None of us used official client. Only reason it was popular is because protocol was reverse engineered and there were clients for everyone. This is just capitalizing on ICQ name that many of russians feel nostalgic about.

I still remember my 7 digit invisible vanity number.

I think the point is that people still remember the ICQ brand. Whether they did or did not use the actual ICQ client 15 years ago is less important.

Sounds like Russia is trying to take a page out of China's playbook with TikTok

Just to make it clear, telegram also tied to the russian government, and they developed telegram based on the message protocol from website vk.com which also owned by mail group.

Its just propaganda move to ban Telegram to make it look independent

What are their strong ties to the russian government?

Mail.ru Group is controlled by Alisher Usmanov, an oligarch from the 90s and an old friend of Putin. Few years back Mail.ru group with the help of russian secret services staged a hostile takeover of VK, biggest social network in russia, essentially forcing the founder to leave the country. Since then VK data has been freely available to any russian enforcement agency, or even anyone pretending to be one. In russia there isn't even a pretense of privacy/independence from them, everyone knows FSB&Friends have unrestricted access to their stuff