OK. By that time he is in his 30s and a victorious monarch who already was married to a royalty. With Russia staying out of the binding international commitments, there probably would be a wide variety of possible matches.Depending on how things progress, Alexei may NEED to remarry in mid-1720ies, if Tsarevna Natalia dies on schedule and he is left with a single heir to the throne (before that, Natalia can be viewed as spare if you squint).
Speaking of which, with the GNW over what could be Russian options in foreign politics?
Trade interests are more or less pushing toward a closer alliance with Britain but not necessarily all the way to the binding military affiliations.
The Ottomans remain a potential problem which mostly shapes Russian interests in the PLC (not letting a French candidate to taKe a throne) and forces alliance with Austria (in OTL since 1727) and a wish to prevent a pro-French candidate to take the PLC throne (hence involvement in a war of the Polish Succession). The whole thing with the Ottomans during that period is hinging upon the Crimean raids and Ottoman unwillingness/in capability to stop them. IIRC, in OTL in 1736 the Ottomans did not strongly objected against Russian “punishment” of the Khanate but capture of the Ottoman-held Ochakov was a different issue. So, if we take Ottoman behavior for granted, then the war is a matter of time and alliance with Austria is logical.
There are certain domestic things which could be done differently realistically to produce different results in a coming war with the Ottomans.