Sending NATO in fundamentally breaks the treaties upon which the organization was founded. NATO isn't a joint military force to send to places for freedom and democracy, it's a defensive organization. Without an explicit article 5 declaration from a current member state against a specific threat for a specific reason, a deployment of NATO would be undermining of the organization's mission in itself, putting in question whether NATO is there to protect its members or just to be used as a cudgel for potential inconvenient threats because the alternative is a financial strain.
Interventions like this, such as the 2011 intervention on Libya to enforce UN resolution 1973 will fuel arguments that NATO is altering its mission from defending its members to participate in US led (or in this case also French led) interventionism. Upon such a time where threats are no longer direct as is the case of the current Russian invasion of Ukraine, this will have implications on the future of the organization and questions will be made about its purpose, as it has happened before after the fall of the USSR. Ultimately NATO's mandate must be upheld and strictly followed, for the sake of the treaty. At least that's the opinion i share.
I'm thinking a terrorist attack of this magnitude with the amount of collateral casualties it had will have international implications that reach far beyond convincing Hezbollah from escalating into a war, if it's actually going to achieve that at all. We're talking about a terrorist group, not an army. Personally i think this will probably just delay it and strengthen their resolve to actually go to war and be even more cruel. Terror groups thrive in terror conditions. The strongest military force on the world couldn't make a dent in terrorist groups operating in the middle east. Peace and stability, however, destroy terror groups.
I'm pretty sure everyone has realized that further atrocities are not the way out of this war. I just hope the belligerent parties can realize it faster and start coming to terms that they will have to share the land and make concessions. Until then i guess we'll keep seeing innocents die for motivations that make less sense each time, like Fatima Abdullah, who was just 9.