I'll add my travel experience, with the I-130 filed and pending, I made three trips 2025, staying over a month each time, travelling on an ESTA from the UK.
I have Global Entry so usually don't have to speak to anyone beyond to confirm foods I'm declaring. But on one trip the machines weren't working properly, so spoke to the officer as one normally would.
He asked length of stay and reason for the visit. I told him to visit my spouse, he asked why we didn't live together and I explained we were waiting for the visa application. He asked who was moving where, and I told him I was moving to the US.
The officer stamped my passport and I was on my way 😀.
Additionally, on one trip we went over the land border to Mexico for a week. Returning using the regular lanes at the border itself. There they simply took my passport briefly to scan/swipe, and asked whether I was visiting, and where I was leaving from, and that was that, we were waived through.
No further questions, despite travelling with my US spouse.
At the security checkpoint a short way inland, they asked only my mode of travel authorisation. I told them ESTA Visa Waiver and they were happy once again.