My understanding is that while both countries are "obviously" at war, neither country has officially declared war on each other.
So, according to each of (1) Russia and (2) Ukraine, are they officially at war with each other?
In practice and under customary law, a declaration of war is not necessary for a state of war to exist. It suffices for one of the parties to make its intentions clear by actually commencing hostilities (source).
Using weapons like tanks and others similar, on both sides, firing live ammunition, with multiple combatants and also some civilians killed on both sides, it is likely more than enough of hostilities.
While there are some laws in various countries how the war could be declared, this is probably more for the case when the war is first declared and only after that the hostilities follow.
Ukraine seems recognizing the war state no question (see their official site). Russia used to call the events "special operation", even if this is now somewhat eroding and sometimes all "collective West" is named by them as being in the state of war against Russia (source). The "special operation" has been declared in V.Putin's speech, including that it will be the military one.
P.S. A country may also declare the martial law internally, suspending many standard civil liberties and making global mobilization possible. Many countries have rules allowing this transition when needed. This is not always done during the war and may be done without (like in the case of natural disasters), so seems irrelevant.
Here's a discussion of the matter
Why Declarations of War Matter
(National Security Journal, Harvard Law School)
My understanding of the matter is that a formal declaration of war means the participants are quarantined from the outside in the sense that any third-party involvement - even so much as sheltering or supplying - is treated as joining the conflict in an actual state of war by the third party.
A formal declaration by a democratically-elected government should also be treated as cover and permission given by the people for not only engagement in the war, but for the conscription of their services; and that such conscription should be considered off-limits unless or until said permission is first given by the people, by, in, and through the formal declaration.
Failure to adhere to that principle will generally lead to a "Mr. President's War" situation, where it eventually peters out due to the lack of support and cover given by the people and where it all lands on the shoulders of that one leader as their onus; even more so, if any kind of conscription is involved. Contrast that with the situation in World War II.