Ideally, if you’re looking to ride both flat pedals and clipped in, you’d have a matching set of shoes and pedals for both applications to have the best setup for each. I have to agree with the comments about single-sided pedals like the Shimano options mentioned - they aren’t great flat pedals and protrude too far when used on the other side.
I also like a lot of the Giro/Specialized SPD shoes, they’re really well built and both brands offer mountain bike shoes with Vibram soles, which are amazing to walk in and have the traction of a hiking boot. If you end up going the clip-in route, definitely check out the Giro Terradura or Specialized Rime shoes.