Our marriage has been very stable for four years, but recently my spouse’s phone has been acting strange. They are constantly texting a coworker and barely puts their phone down. When I asked about it the other day, they said, “We’re talking about work,” but for some reason, this always happens in the evening… I’m suspicious, but am I just being paranoid? What would you do in my position?
So how long do these business conversations actually last? For example, are they just a couple of messages, or do they drag on quite a bit? Also, do you know this colleague at all, is it a woman or a man, for instance?
When talking to your partner, try to speak openly without blaming them. If you have doubts, instead of stating them directly, express in detail what is bothering you in your relationship. If there is no healthy communication regarding such doubts, the issue may escalate further.
So you’re saying the guy is constantly messaging in the evenings and can’t seem to put his phone down. It feels to me like there’s a pretty high chance there’s something going on outside of work. Of course, I can’t say for sure, but I’d suggest taking a look; it doesn’t seem like a coincidence.
I think you should just be direct and ask again. Clearly express your discomfort, don’t bottle it up. If necessary, ask more specific questions like who that coworker is and what the messages are about 
Yes, that colleague is a woman by the way. I’ve heard her name a couple of times before, but I don’t think they’ve been in any non-work-related organization together in a special meeting or something. I couldn’t catch their messages, but she always seems anxious and hangs up the phone right away.
Look, marriage is a partnership, and the real problem is that your spouse is not being open with you about something so important. The “work excuse” is something that’s constantly brought up; you need to set boundaries. They have no right to dismiss your concerns. Speak directly and question their behavior.