Thankfully, you gave an example of what being "a prayer squirrel" means. What remains outstanding is a clear understanding of what it is to sin. Some answers have claimed that one's will must be involved in committing a sin - that a sort of decision has been made to do something wrong in God's eyes, or that one has chosen to lapse rather than to resist a temptation to do wrong. Or that sin is a transgression of God's commandments. Ah, well, there are a couple of problems with viewing sin that way.
First, it does not take into account sins of omission. It only deals with sins of commission. Yet the Bible tells Christians that if they fail to do something good, they have sinned (e.g. if you have two coats and see someone without even one, you should act.) See also Jesus' parable of the good Samaritan.
Second, There is no command against being detracted whilst in prayer. We have poor Eutychus who fell out of an open window and died, having falling asleep during a lengthy discourse of Paul, but Paul raised him back to life! (No mention of whether a long prayer was going on then...) Eutychus succumbed to physical tiredness, not to sin.
Then there's the case of the disciples falling asleep at night while Jesus was praying in the garden of Gethsemane. Were they accused of sin? It distressed Jesus, and they felt ashamed, but even though we may well consider them to have sinned (failing to keep Jesus' command to them), their physical tiredness was the problem, not any exercise of the will. "The spirit is willing, but the flesh is weak" (Matthew 26:41). But if anyone wants to consider weakness of the flesh as sin, I would not disagree. I think that is true.
So, let me put my hand up immediately to admit that due to weakness of my flesh, I am sometimes guilty of having my mind wander while in prayer (either listening to others' prayers, or saying my own private ones). It is perfectly possible to sin in holy matters, and prayer is a most holy privilege and duty. I have to confess that to God and seek forgiveness when it happens (for it is a case of 'when ', and not 'if'.) Yet it remains a comfort to me that saints of old have turned to God in prayer when unable to sleep, and who knows but that their prayers led them into sleep? Could there be a better way to transit from wakefulness to sleep than whilst in prayer? That way, one's last waking thought was on God and (when one prays the minute they are awake) their very first wakening thought is on God.
None of us can judge another on this private matter of prayer. Colossians 4:2 says, "Continue in prayer, and watch in the same with thanksgiving." A.V. So, thank you for raising this question, which admonishes me to be more diligent, so that I sin not in holy matters.