[mattbrewsbytes]

You didn't ask about productivity, you just stated that you did nothing for your software engineering work. This implies you have other types of work, possibly meetings, documentation, helping out others. Did you do those things? Then state that, many of the little things that happen add up and if you get slammed with a lot of that then you may not write any code that day. Did you spend hours troubleshooting some weird bug? Maybe feel imposter syndrome about it like others might be better at solving it and don't want to mention that, I would mention it to your manager. Long hours on tough problems are learning opportunities, things you'll likely remember for a career.

If you are distracted and didn't do any work at all for your employer, just tell your manager you need to put in a day off request for yesterday, got distracted with "life" (bingeing a show, grinding levels in a video game, staring at a wall, etc). Own up to it because if you end up letting it slide, its a slippery slope into that growing to a week of doing nothing and covering for yourself with varying excuses. Sure a day here or there might go unnoticed but eventually this will catch up with you if you aren't being honest with yourself. Then time goes by and someone looks at your outputs and sees next to nothing. A nothing day might be a sign that you should schedule time off every month/quarter, if you have one planned you'll look forward to it more and that might motivate you to get your stuff done.

Software work can be extremely boring at times and being remote has lots of potential distractions. Another perspective could be asking yourself if remote work is a good fit for you personally? It isn't for everyone.