There are no solid polling data on how many Russians say Alaska is rightfully theirs. I was able to find the following results, indicating that between a quarter and a third of Russians say that Alaska should definitely be Russian. These results are highly suspect due to small numbers of respondents and no evidence of random sampling:
Open to: All, detailed results viewable to: All. Participants: 187
Should Russia own Alaska?
52 (28.4%) Yes, Alaska should definitely be Russian (I am from Russia)
40 (21.9%) Maybe, if America falls apart, then Alaska will be reunited with Russia (I am from Russia)
37 (20.2%) No, Alaska is American (I am from Russia)
3 (1.6%) Yes, Alaska should definitely be Russian (I am from Alaska)
2 (1.1%) Maybe, if America falls apart, then Alaska will be reunited with Russia (I am from Alaska)
0 (0.0%) No, Alaska is American (I am from Alaska)
10 (5.5%) Yes, Alaska should definitely be Russian (I am neither from Russia nor from Alaska)
8 (4.4%) Maybe, if America falls apart, then Alaska will be reunited with Russia (I am neither from Russia nor from Alaska)
17 (9.3%) No, Alaska is American (I am neither from Russia nor from Alaska)
14 (7.7%) Other opinion (specify in comments)
Alaska is Russian territory? (Poll). September 25 2014: https://politichanka.livejournal.com/229306.html
The idea of the return of Alaska has been circulating both on Russian Wikipedia and in the Russian Parliament (Duma) at the top level.
Interestingly, a popular song "Uncle Vova, we are with you!" got 754,000 views on YouTube and features a call to return Alaska to Russia: "We will return Alaska into the harbor of our Fatherland!". The song is performed by a chorus of children led by an ex-Russian MP, now a vice-mayor of the city of Volgograd, Anna Kuvychko. Uncle Vova is a reference to Russian President Vladimir (Vova) Putin.
"Alaska is ours!" billboards (reminiscent of "Crimea is ours!") are also being put up across Russia.
The Speaker of the Russian Duma Vyacheslav Volodin threatened the US to return Alaska [to Russia], if that country continues to manage the international assets of Russia. He mentioned this at the plenary session of the lower chamber of the parliament.
"There is such a region, Alaska. And let America, when it tries to manage our resources, ponder that we too have things to return", said Volodin.
Volodin threatens the United States to return Alaska. Business Online. July 6, 2022: https://www.business-gazeta.ru/news/556111
Oleg Matveychev, a member of the Duma, told Russian state television earlier this year that Russia should seek the "return of all Russian properties, those of the Russian empire, the Soviet Union and current Russia, which has been seized in the United States, and so on."
When asked if that included Alaska, Matveychev responded that it did.
Putin Ally Warns U.S. Russia Could Start Military Fight Over Alaska. BY ZOE STROZEWSKI, 7/6/22: https://www.newsweek.com/putin-ally-vyacheslav-volodin-warns-us-russia-reclaim-alaska-1722342
A separate upsurge in the popularity of the topic of the return of Alaska occurred in 2014, immediately after the territorial expansion of Russia [to include Crimea], which was not recognized by the majority of the world community.
The Return of Alaska. Russian Wikipedia. https://ru.wikipedia.org/wiki/%D0%92%D0%BE%D0%B7%D0%B2%D1%80%D0%B0%D1%82_%D0%90%D0%BB%D1%8F%D1%81%D0%BA%D0%B8
A popular song: "Uncle Vova, we are with you!": https://www.youtube.com/watch?v=3ZZJJ1k8xAE
The billboard "Alaska is ours!" in Russia:
Tweet by NEXTA, "the largest Eastern European media". July 7, 2022: https://twitter.com/nexta_tv/status/1544997154204401666