No heat, not common issues

I have a 2001.5 Audi S4 b5 with a brand new water pump, tstat, coolant sensor, and did a heater core flush with CLR. I always read the same things; air in the line, clogged heater core, and to check the heater core hoses for heat.
The problem is neither of my hoses are hot and I only get heat under engine load. I decided to bleed the heater core tonight and ran the car from cold, to everything being up to temp. I had the passenger side hose backed off and no coolant was even going through the tube at all. I know I have a faulty Aux pump since it leaks and sometimes makes a strange noise when I turn the car off. I have read that the aux pump has nothing to do with the heater core, and I have read it does.
I know this topic has been beaten into the ground, but all of my google searches come up with things that dont match my exact issue.

Please help.

OK so let’s take this in stages and get thus fixed for you. You have the top heater hose and the bottom. The passenger side hose should be the after the heater core. You want to check the to the heater core hose. Pull them both off but fill the coolant tank. What I have done to inspect heater core issues is I loop the heater core hoses together using clear tubing and I watch to see if water passes through them. Do you think you can do that or would you want me to explain more on how. I would start there. Also do you know where the bleeder screw is on the coolant system and is there fluid at that location.

Give some answers to those questions and we will help you fix the issue.

Bleeder screw by tbb is stripped, I decided to see if I had alot of flow through the heater core before I really messed with that. Turns out I have zero flow through heater core unless I give it some gas, otherwise noting goes through the core. Could this be related to the aux pump? Ive heard that is just a after run pump, could it also be there to help the flow to the heater core?

It could be an issue up there it really sucks having that bleed screw go bad. I would think if the flow only comes when you hit the gas you might want to check your water pump. You might have a broken fin on the pump.

Curious if you have tried sliding the inlet heater core hose off slightly while the engine is somewhat warm/hot?

Usually there is a tiny hole on the hose itself and if you unclamp the hose, and pull it off just a little bit, it’ll vent air. Chances are good it’s just air that needs to be purged for it to flow correctly.

Would be good to connect a hose to the heater core inlet, fill with water until it starts to come out of the exit. Unclamp the inlet hose, start the car, slide the hose back slightly so it can vent air , but little to no water/coolant. Lots of caution about hot coolant and stuff. I’ve had to do this several time though to get the heat to work on my a4.