My gut tells me that the balance of power is not at all as "equal" as it's claimed ("both sides have nukes") but there is enough uncertainly on all sides to want to test it.
The "usual" rules of gradual escalation probably apply. Of course, it's best to avoid any escalation because it can be an uncontrollable situation.
If a country is experiencing mass psychosis and wants to commit murder-suicide, it doesn’t really help that the other countries have nukes too
I wouldn't be so sure about this. He has working hypersonics and this advantage would last very short time. Currently those hypersonics can't be even detected in time before they hit their targets and there is no real defense against them. He might just launch 100-200 of them with 100kT payload at military/strategic targets in Europe at the same time, level down parts of countries without any response outside submarines or US strategic nukes (their flight time is in minutes anywhere in Europe, insufficient time to react), and then given Europe would be written off for a century, he can try to negotiate terms with the US, assuming MAD is given if diplomacy fails and there is a proof already (destroyed Europe).
He perceives UA effectively in NATO (given heavy arm supplies) as an existential risk for Russia, so he might go all in.
It does, but similar risks have come by before (in S Asia). India & Pakistan had a full confrontation in 1990s, when they were both nuclear capable & backed by Russia and US respectively. People at the helm of warcraft perhaps know where to draw the line. It is highly unlikely Putin will use tactical nukes or pre-emptively strike US/EU, no matter how grim the war looks.
People do not realize that the game of brinksmanship has played out several times in the past. We empathize Ukraine because news coverage & social media have brought the sounds of guns and rocket right to our doorstep. Horrific war crimes have happened, countless people died & children orphaned in Kosovo, Palestine, Kashmir etc. - but we can't connect with it because we don't see it flashed in the daily news.