Russia has stated (prior to the formal invasion of Ukraine) that NATO poses an "existential threat" to itself. Interestingly, a paper from 6 years prior evaluates whether Russia is an existential threat to NATO. The European Union also has a collective defense clause (that has never been tested) that functions similarly to the NATO defense clause. Both organizations' clauses do mention that the alliance is a defensive obligation.
Obviously, there is large overlap between the organizations. Notably, the EU is missing the US and the UK. In a recent statement, Russia officially states that the US is an existential threat so the lack of the US in the EU is likely a deal breaker. This brings the question then is the EU even a political body that can influence Russia (nevermind deter it from an invasion)? Ignoring the fact that Russia has significant influence in the EU, even to the point of members like Germany, France, and Austria stating that US sanctions on Russian energy are illegal in 2017, can the EU actually pose a threat politically? Sanctions do not seem to be deterring Russia from further invasion and Russia specifically calls out NATO expansion as red lines but seems to ignore similar talks about expanding the EU. It does help to keep in context that the de facto purpose of NATO on creation was to counter the USSR (whose successor state is now Russia), whereas the EU is an economic union with defense tacked on later.
There seems to be some confusion on what the question is asking so I'll clarify what a "political threat" means. Entity A poses a political threat to Entity B if A can influence B to the point of acting in the interests of A instead of B. Regardless of official statements, many countries are de facto in this situation. North Korea is an example of B where China is A, in a protectorate/vassal relationship. Turkey and the KSA are in such a relationship, but in a different type of relationship (regional hegemony). NATO and Russia are in such a relationship, where NATO can essentially strong-arm Russia.