"but this sounds like a muddling of what is required for arrest and what is the evidentiary standard for resolving a civil case in the US."

I remember seeing that the standard for what was reasonable search and seizure in my state was set at preponderance of the evidence. It seems to be in line with other states/fed where you need evidence supporting that the crime has been committed or the object exists in a specific place. This can be, and often is, just an affidavit from the officer(s). Being a one sided process, being more likely than not is satisfied if there isnt an issue with the affidavit like missing element of the crime or unrealiable testimony. The problem comes up when the judges aren't viewing these with an open mind or to the standarss that states set (often these are handled by magistrates that do not hold a law degree nor have passed the bar). Often times the elements of the crimes defined in statue haven't even been claimed to have been met in the affidavit.

As an example, there might be someone operating a still at their residence. Just the sight of a still does not provide probable cause (only reasonable suspicion, and even that could be arguable). For probable cause to be met, you would have to prove that it was used for alcohol and that the person didn't have a fuel distillation permit or was selling it, etc (and probably one or two other small things in the statute). This is specific to my state. Other states may have more stringent rules about even owning a still.

"I think realistically the trigger for a search or an arrest is going to be much less than what is necessary to successfully convict in a criminal case or to prevail in a civil case."

It is less than the standard for conviction. All it needs is to show the elements of the crime have been claimed to have been met in the affidavit. Although they aren't even meeting this standard in every case. Or in some cases the officers have lied or made mistakes.

It's not exactly the same as a civil case since the warrant process is ex parte and does not need to consider defenses to the charge. It's just the same level of proof but applied to one-sided testimony. For example, you might have shot someone in self defense and the witnesses all agree it was self defense. They can still charge you (in most states) and make you prove that defense in court. You could get into some malicious prosecution stuff here, but according to probable cause you have satisfied all the elements of the crime and can be charged. Proving your defense then happens at the trial.

IANAL either, but have some criminal justice background. These are just what I have seen as it applies in my state.