I just wanted to double check with the great minds on this forum if I get this right.

Synapse units: it says that " As last step before the combat phase ends, if the synapse unit is still at a planet , return the synapse unit to its HQ, maintaining its state ."

Say you play Tyranids, and it's the first turn of the game and you deploy all your stuff, send warlord to planet 1, opponent sends warlord to planet 1, and a battle is fought at the 1st planet only. But, you've sent your synapse to say planet 4.

After the battle is over at 1st planet, but before the combat phase ends at planet 1, does the synapse unit return to HQ, even though there was no battle at planet 4?

Thanks for the clarification.

After the battle is over at 1st planet, but before the combat phase ends at planet 1, does the synapse unit return to HQ, even though there was no battle at planet 4?

Yes, but be careful of your terminology and timing here.

The rule is that the Synapse unit will return to HQ as the last thing that happens before you move on to the HQ phase, even though there was no battle at planet 4.

There is only one "Combat Phase" for battles at all planets, not one separate combat phase for each planet. That means the Synapse unit at planet 4 will not head back to the HQ when the battle at planet 1 is over. It will stay at planet 4 until you have formally checked each planet for a battle and moved on to the end of the combat phase.

So remember that ending the battle at planet 1 does not end the combat phase , even if both warlords were there. As a practical example, you have the chance to play Actions between the end of the battle at planet 1 and the end of the combat phase - so if you're playing against Aun'shi in particular, there is a chance that the opponent's warlord could move to planet 4 so that there is a battle there; a battle your Synapse unit would not miss because the combat phase hasn't ended yet.