I would say the wording is clear, but also counter-intuitive. A clash with expectation causes people to read what is not there. If people see the word "blade" and "scimitar" they expect those things to be part of the mechanics, which they are not. Also, the average level of reading comprehension is just, really bad, universally. Speaking as someone who sometimes teaches it.
There is also a general issue with 5e of people being unable to separate fluff text from mechanics. Typically, in 5e the first line of a spell description is fluff.
Because many of us, and I'd argue rightly, believe the fluff is as crucial as the mechanics and there to give you the intent of the mechanics and the guideline for how to adjudicate the mechanics. For example if the fluff says something glows blue and the mechanics don't mention a radius of light, I as the DM am being told to make a judgement call on how much it glows because it does in fact glow despite them leaving out a radius of light. The game is full of those judgement calls and that doesn't disappear just because it's a spell text.
Here a DM is asked to adjudicate how the Improvised Weapon rules interact with an "evoked fiery blade" that is "similar" in size and shape, but not necessarily similar in weight or speed, to a scimitar. And you must hold this thing (unclear what it is you're holding really) in a free hand and if you let go of it with that hand it disappears.
Now to you think that's enough data to be "clear" on how the Improvised Weapon rules would work with it. I don't. Improvised Weapon rules ask three questions: 1) is it an object, and 2) is similar enough to an actual weapon and can be treated as such for proficiency issues, and 3) what damage and damage type does such an improvised weapon deal (default 1d4 if there is no further indication.)
My answers to #1 is yes, since you're holding something. And the something you're holding doesn't seem to be fire since you don't take damage yourself so I assume it's an object like a pommel or similar-enough to an object to qualify as one. But I can see a DM arguing no, since it's an "evoked fiery blade" and already some in this thread have argued it's energy and not an object. So already to me that's "not clear."
My answer to #2 is lacking guidance on weight and speed, and the blade being described as "fiery" which disappears easily, and the rule of cool being what it is, I am going with the "lightsaber" sort of description and therefore I don't think it's "similar enough" to an actual scimitar to get proficiency bonus unless you have a feat that gives you proficiency with improvised objects. Others disagree in this thread and thing it is, so again I'd say that's "not super clear" and reasonable minds can differ on that question.
Finally my answer on #3 is the spell tells you the damage done by being hit with such a thing, and you're being hit with such a thing, so that's the damage I'd use. It might not be "similar enough" to a scimitar for proficiency, but it's sure "similar enough" to a fiery blade to determine that's its damage. But again, others in this thread disagree and would go with either the default of 1d4 (fire damage), or with the scimitar damage. Which again I think is all reasonable, and the rule isn't clear requiring these judgement calls.
My rulings are influenced by the overall DMing rules of "is it balanced" and "is it cool and fun for the players." It's balanced to allow extra attack with this otherwise very sucky spell. And it's cool to find a way for people to want to use this lightsaber-like spell where otherwise they simply wouldn't choose it.
What part of this did you think was clear or did you think I was not comprehending well, and why do you feel separating fluff from mechanics is more helpful than reading them together in this instance?