Symbiotic Entity only applies to melee weapon attacks.
Symbiotic Entity says:
Your melee weapon attacks deal an extra 1d6 poison damage to any target they hit.
So it depends on the particular spell. The given use case, thorn whip (PHB, pg. 282) says:
Make a melee spell attack against the target.
This is a melee spell attack, not a melee weapon attack, so Symbiotic Entity would not apply. A spell would have to specify you are making a melee weapon attack for it to benefit from Symbiotic Entity.
For example, a druid using shillelagh (PHB, pg. 275) would benefit from Symbiotic Entity:
The wood of a club or quarterstaff you are holding is imbued with nature’s power. For the duration, you can use your spellcasting ability instead of Strength for the attack and damage rolls of melee attacks using that weapon, and the weapon’s damage die becomes a d8. The weapon also becomes magical, if it isn’t already. The spell ends if you cast it again or if you let go of the weapon.
Since you would be making your attacks with a melee weapon (a club or quarterstaff), Symbiotic Entity would boost the damage of those weapon attacks.