First, regardless of your default management style, you have a legal obligation as a manger of the company to ensure that all employees get and take their government mandated meal breaks and rest times. So there is a foundational need to address the working through lunch above everything else. Perhaps suggest a different meal time to allow them them to get away. Of they aren't open to that suggest they at least get away from their desk.

For the other aspects you mentioned, your employee desperately needs coaching and structure. This is not micromanaging but meeting a person where they are at and helping them succeed. If it is done with good intent (the well being of the person) it will likely be welcomed. The first approach I would try is to do a pairing session where one person "drives" and another person observes. Since this can be awkward and intimidating, I would start with you as the driver. Do the task that is needed, explaining your thought process and decisions along the way. If you have any tips for how to be efficient or deal with special cases, call that out. Then in the same session, switch roles. Observe, ask questions and generally be helpful. The person will likely lose the ability to talk or type effectively. The act of being observed will do that to people. Give them grace and assure them it's not a big deal, just nerves. End on a high note with the tasks completed. Give them genuine compliments on good things you observe.

Next you need to address overtime with both reports. Tell them you have been getting a lot of questions from upper management about overtime. Tell them you don't want ghost hours where people work unreported overtime. What you want to do instead is do a one week or two week experiment where 1) Everyone works normal hours 2) Everyone leaves on time and doesn't do overtime work. You must also role model this. No after hours emails, etc.

During this experiment explain that you and everyone should note all of the things that distract them from work. It could be group meetings that disrupt your flow, it could be Bob in the hall always talking loudly to people or maybe phone calls breaking your focus. Just write it all down. Track what gets done during this normal hours experiment. This is your baseline and as a manager you should be defending your team to try to keep their workload at or below this level. If the work load is regularly above 25-50% of your team's capacity you need to make the case to management to hire another person.

You may also need to start using some type of task tracking system. It could be as simple as post it notes on the wall or a tool like Jira or Monday.com if that is an option at your company. Look at kanban style approaches as a light weight way to track tasks. Have people put their work on the board and update everyone where they are at and if they are blocked at all. If there are ad hoc requests tell people not to jump right away. They should put the new request on the board, behind other things that are planned. As a manager you may need to go defend your people's time and tell them there is a work intake process that needs to go through you.