This bug has been around since the issue of the first patch for Supernatural. SN introduced a collection journal and plants is the last page of the journal. I understand the if you buy and install SN the proplem is rectified. I do not, and will not, have SN. (I simply do not want the main content of this EP). So I have had to try to find a workround. (I believe there are third party mods which fix the problem, but, I never use mods, so can't tell you any more about that method of fixing the problem.)
I have not found a complete workaround, but, I have worked out how to have your sim able to harvest at home and in one other location if that is of any help to you.
Start your new sim or sim family. Whatever you do, do not allow the sim to collect anything or buy anything collectable in their home town until after the sim has been abroad. Decide which location you want the sim to harvest in. I usually choose France as there are a lot of harvestables there and I like to make nectar once I have built a vacation home.
Go on vacation (I usually take the 3 day minimum vaction on the first sim day of play.) The first thing to do when you arrive at the destination is to harvest something. It does not matter if you scrump from someones garden or plunder a community lot, just so long as you harvest one plant. This will initialise your collection journal and you will get a "plants" page for that town.
Unfortubately, the other two towns will never get a complete "plants" page and you will continue to have the problem in those towns.
If your sim family contains 3 adult (or teenage) sims, you could send each to a different location and have the abilty for one family member to harvest in each town, though, I do not bother with this prefering my sims to be able to harvet collectively. Sadly, child sims are a problem as you cannot allow them to collect anything until they have aged up to teen and travelled to their chosen harvest town if you want them to be able to harvest while on vacation.
I am afraid that Lez Bee-Ann will never be able to harvest abroad unless you buy and install SN or find a mod. Or, of course, EA fixes the bug!