Help, how do you learn to trust again after an affair?

I found out by accident last week that my husband of 23 years has been texting a woman from a company, that the company he works for has dealings with.
When I saw the messages I was so shocked, I couldn't breathe and felt physically sick.
The messages were calling each other darling, making arrangements to meet, asking if each other had woken up yet etc. The woman also sent him a highly sexual video clip.( not of herself)
When I confronted him about these messages he said it's just someone he needs to keep good contacts with to get a big project..., he said nothing sexual has happened, they just send messages and meet for dinner and that he is just mirroring her flirtatious messages.
He said he loves me and only wants me and is just using this woman to get a big project. He was really upset because I had seen the messages and I got so distressed.
I'm still in shock and feel really upset and uneasy about this bizarre situation,
I don't know if I can or should trust him anymore. He says the project will be finalized in July then it will all be over.

Has anyone got any advice?

Wow that really sucks. I would be shocked and appalled. I don’t know if I would be able to trust him. That “I’m just using her for a project” doesn’t make him seem like a good person, even if he’s telling the truth which I tend to doubt. Being sexual with someone is still cheating even if he hasn’t actually had physical sex with her...yet.

Well since he’s also lying to you I’d be doubly insecure - his excuses show no respect for you.... good luck 🙏

Thanks for your reply. I'm not sure who he is anymore.
As you said, it doesn't make him look like a very good person using someone like that, if of course that is what he is doing.
I really don't know what to think

that he tried to pass if off as business relationship stuff... just says something about his integrity. It's bs if anyone tries to tell you "mirroring flirtatiousness" is an acceptable way to conduct a business relationship.

I'm worried that if he's lying like that about the discovered texts, how much more really is going on.

They just have dinner together?

And there are sexy videos and texting and he is just using her until his
project is over?

I would make sure you are financially secure before he realizes you are
smarter than he thinks you are.

He's a predator, honey. Protect yourself.

I'm more familiar with couples going out for dinner when sales pitches are the name of the game. Usually it's an invite the spouse scenario.

I, personally, don't believe I'd give an ounce of trust about 'are you awake' messages.

Sounds like a tiff over the discovery of aforementioned texts? That [discovery] typically is fueled by feelings of disconnect to begin with. Which isn't typically some shortcoming in character.

"Upset you saw his messages" means "upset you were up to him"
If he can manipulate another woman, don't you think he can do that to you, too?