I think if she'd left her handbag behind and disappeared on the walk, it would have been quickly discovered by her partner and LE. Then there's the note, one wouldn't leave it out until actually leaving, nothing more awkward than walking in on your partner reading your 'I've run away from home' note. Not to mention the mysterious thousands of pounds that she surely wouldn't take dog walking.
Here are the questions that stand out in this case to me, aside from the obvious one of what happened to her:
1. Was it her partner who claimed to LE that they were recently engaged, though no one else has publicly confirmed it?
2. Why would she leave him a note saying she was taking time to herself in Broadstairs if they'd recently got engaged?
3. Why didn't he become concerned about her until several days had passed - recently engaged people do not go days without news or contact.
4. Why would she take her phone but keep it turned off even as she left the house.
5. What's with this large sum of cash that she may have taken but no one's sure.
6. Why, after being missing for a month without turning her phone or accessing her money would he write her a note, asking her to "listen carefully". "We promised each other 30 years please keep that promise and come home. Whatever has happened, wherever you are I will come and get you and Boris". Although the papers called it 'heartfelt', it actually sounds extremely possessive to me.