Rest Days?

Walking should be fine. To some extent, you can use how you feel as a guide, but how you feel after multiple weeks of a particular schedule/routine could have a different cumulative effect than just one week's trial.

I've been working out regularly for almost 20 years. I usually take one formal rest day per week, which may include an easy walk or some yoga, or some other non-fatiguing non-stressful thing. (The definitions of "non-fatiguing" and "non-stressful" will vary some, by individual fitness level and other factors).

At this point, I also know that I do better if I don't do the exact same workout types day in and day out. For example, in season, I usually alternate on-water rowing with cycling, but often include a longer but easy-pace walk (usually about 5 miles) on the rowing days. Strength workouts always have one day between workouts of the same muscle groups.

How much of this is necessary in general? Some. How much of my routine just works better for me this way because of individual characteristics, like joint conditions, age, fitness level, etc.? Some. People new to exercise, or resuming after a long time off, IMO, should include more recovery time (maybe more recovery days), and increase gradually, for best results. Recovery is when much of the getting stronger/fitter happens, and some types of recovery are specific to the stressed muscle systems used in the exercises (such as strength training).

If someone has access to a formal training plan for their chosen activity (such as C25K for runners, or a good strength program for lifters, but there are other examples), a plan that's appropriate to their fitness/experience level, that's a great thing. Some of the higher-end fitness tracking devices/apps also have metrics for tracking overall fatigue, which can be helpful. Not everyone needs to go that far, but they're good things to be aware of, especially as fitness and goals get more advanced.

I'm a runner who usually runs 5 days a week. I have a dog, so I walk 2-3 miles 7 days a week. On my non-running days, what I do depends on how I feel and how busy I am. Some of my non-running days I just walk the dog, some days I'll also ride the stationary bike, or mow the lawn or do yoga or Pilates or go for a hike. When my body tells me I need a break, I take it.

I don't have a vigorous workout regime; it consists mostly of an hour to 1.5 hrs of indoor biking and rowing cardio, but I do take a "rest day" once a week from the machines. However, I try to get in a 1.5 - 2 mile walk on the rest day. I guess it just feels like a wasted opportunity to me to have a whole day go by where I don't make any investment in my physical well being. Even a half hour brisk walk makes me feel like I did something useful for myself. I try to eat carefully and healthily on the rest day, because I've learned that for myself, the combination of not really doing a workout AND not drilling down on the health and calories of the food can lead to bad behavior.