Could you give me examples of: Parts of plants which taste fruity,
but are not fruits. (The only example I can think of is rhubarb.)

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cashew (not the nut), juniperberry, yew berry, etc BRBR

Iris Cohen schreef
Juniper and yew berries are fruits. They are called cones, but they
contain seeds if they are fertilized.

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They are not fruits (botanically speaking). The berry of yew is an aril, a
later outgrowth. I am a little unsure what a juniperberry is but I would
suppose a cone is as good as anything I can come up with at short notice.
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The fruity part of a strawberry is an achene. The actual fruits are those
little things all over the outside which contain the seeds. The edible
part of a pineapple is also a holder. Our modern pineapples are seedless.
Not sure which part you would call a fruit.
One notable example is the Japanese raisin tree, Hovenia dulcis. The
fruits don't amount to much, but when they ripen, the fruiting twigs become
soft, tasty, & edible.

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As in Cashew you mean?
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Nature is varied and ingenious. Fruits evolve and are further cultivated
to enhance the reproductive ability of the plant. Any part of a plant may
become a storage organ to tide the plant over the winter or the dry season.
This can be leaves, stems, sap, or roots. If they are used to store sugar,
people (and animals) may find them tasty, and possibly fruity.
Iris,

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Well enough, although for a fruity smell and taste some other substances are
involved, in small quantities but with a big impact.

Who knows what people will come up with. They made "meat" from soja and
fungi, so making fruits out of green or white plant parts would not be
unexpected.
PvR