After the Russian Revolution, the Orthodox Church in America became nominally independent of the mother church. The OCA has since canonized saints who lived in Russian America such as German and Petr (the former was also reportedly "venerated" by Patriarch Alexy II). Do these saints enjoy any formal status in the Russian church, or are they only of interest to Orthodox belivers in America?
The process, if one can term it that, by which Orthodox recognize certain people as "saints" is radically different from the practice followed in the Roman Catholic Church.
Recognition of saints among the Orthodox begins first with the local faithful who recognize that person who has reposed as someone who had cooperated with God's grace to the extent that his or her holiness is beyond doubt. As Metropolitan Kallistos Ware writes:
In private an Orthodox Christian is free to ask for the prayers of any member of the Church, whether canonized or not. It would be perfectly normal for an Orthodox child, if orphaned, to end his evening prayers by asking for the intercessions not only of the Mother of God and the saints, but of his own mother and father. In its public worship, however, the Church usually asks the prayers only of those whom it has officially proclaimed as saints;
The Orthodox Church, p. 256
The Orthodoxwiki website describes how a saint is usually "canonized" within a given jurisdiction:
Today, as more clergy and faithful recognize and honor that one amongst them had led a virtuous life of obvious holiness this veneration becomes widely recognized, and the manner of recognition is formalized. This leads to requests, usually through the diocesan bishop, for the Church to recognize that person as a saint. Then, usually an investigative committee is formed to review the life of the person who is being considered for glorification. When the committee is assured that the person has led a virtuous and God centered life, a process that may take an extended period of time, a report is submitted to the Holy Synod of the local Church stating the reasons why the person should or should not be recognized as a saint.
After receiving and considering the report, the Holy Synod decides whether or not to number that person among the saints. If the bishops agree they then have icons painted and liturgical services composed for the glorification of the new saint. If the bishops do not agree, the life of the person may again be considered at a future time after further study.
The formal Rite of Glorification begins with a memorial service for the person about to be glorified, after which Vespers and Matins are chanted with special hymns to the saint, and the icon for the saint is unveiled. The feast date for the commemoration of the new saint is established, and the life of the saint is published. Finally, the glorification of the new saint is made known to the other Orthodox Churches so that they can place the name of the new saint on their calendars.
As the article indicates, once a particular jurisdiction within the Eastern Orthodox Church formally recognizes a saint, recognition is also extended by all other jurisdictions. Hence, Sts. Herman of Alaska and Peter the Aleut - which you mentioned in your question - are venerated as saints in Russia, Greece, Georgia, Romania, etc.