Very little. Do people think Villareal are a huge club because they won it? United have won it recently .. how much did it do for them? Or Sevilla who are now perpetually mid-table after winning it numerous times. It would be a wonderful memory for fans but if anyone thinks winning a EL is a golden ticket for our rep or a rebuild they're wrong.
Getting to a CL final, beating Madrid etc did much more for our reputation as a big, competitive European team. Far more eyes on the champions league and you're trading with the best.
I agree we would look back on the Pochettino years differently if we had won something.
Winning is a habit.
Getting to a CL Final and losing only cemented the idea that this club doesn't know how to get over the line and actually win things.