Negotiating for a pay raise: I might not be worth what I’m proposing (to them)"

Hi Coaches,

I have a situation where I currently have a contract with Company A. This contract will end as of 6/5 and we are in discussion about renewing it.
The situation is a bit complicated because my contract is with Company A but I’m being fully compensated by Company B (they pay my salary).
This is because company B doesn’t have an entity in the country I live in and I have known Company A for a while now. That’s how I got this job.

I have a lot of mind drama about this negotiation and I’m thinking it’s because Company A and Company B are very different.
Company B is very easy going and we have a good connection. I already had a casual conversation and they are happy to give me a pay raise.

On the other hand, Company A wanted to hire me as a full time (not as a contractor) and they have even talked about a pay cut if I were to only take work for Company B. They are also a bit intense and serious. Intellectually, I know that this is just a C but I can’t get through it.
I feel anxious when I have to discuss this with Company A and it has caused me to go behind their back to negotiate directly with Company B.
I thought that would make my chances of getting a pay raise higher.

I did a model on this:
C: contract ends on 6/6. Had meeting with company B.
T: Company A might say no to my new proposal
F: anxious
A: not setting up meetings with company A, ignoring direct discussion with company A, discuss with company B and see if they are happy with raise, go behind company A’s back
R: I’m saying no to my new proposal ahead of time?

Not sure if I got the result right. Even after making this model, I kept asking myself a bunch of questions.
When I asked myself why I’m not confident asking company A for the pay raise, I realized I had the thought:
“I might not be worth what I’m proposing (to them).”

I don’t have this thought when I’m speaking with Company B.
But because of the vibe I get and the character/culture of Company A, I get anxious and I act small.
It’s very similar to when I have to interact with people that are intimidating or don’t like me.
I can tell that I people please and negotiate in a weird way.

I want to be confident when I do the negotiation but I can’t seem to find a good ladder thought.
Some intentional thoughts I was able to come up with were:
-The worst that can happen is they say that they can’t pay the raise.
-They might even say they want to lower salary and that’s ok.
-They try and find some other candidate and that’s ok

But these thoughts feel too distant. I’d like some advice on a ladder thought that is closer to where I am now.
Any advice would be appreciated. Thank you!