They are different abilities and they work slightly differently
Your interpretation is correct. A changeling PC has no restrictions on the creature type they can change into, only general body shape and size. Doppelgangers can change their size but are restricted to the humanoid creature type (but appendage arrangement is limitless1). Whether you think the humanoid restriction makes sense or not, it is clearly there and there is simply no way to otherwise interpret it. Similarly, the size differences are also clearly written and unambiguous.
It is clear that the Changeling PC's ability has slightly different capabilities than the Doppleganger monster. Note that these two abilities don't even have the same name and appear to have no connection to each other at all beyond beyond superficially similar.
The two abilities were written at different times and published considerably far apart for two different types of creatures (PCs and monsters). But that is not at all unusual, in fact it is more unusual for monsters to have exactly the same ability as a PC. Monsters follow many different rules and have many different abilities, some that are kind-of similar to PCs but not really (multiattack versus Extra Attack for example).
It might be worth noting that the PC version is based on the "change appearance" ability of the alter self spell. Whereas Shapechanger is ability that many monsters have and each version of it is slightly different. Though actually the Death Slaad has the exact same variation as the Doppelganger.
No further clarification has been made that I can find, but I also don't think any clarification is needed. There's simply no reason the abilities would be expected to be the same.
1 - Or limb-itless you might say.
You also don't need to sleep, and don't suffer exhaustion from lack of rest.
I believe this could be abused.
Suppose a Slimefolk Sorcerer/Warlock uses Flexible Casting to convert Warlock Spell Slots to Sorcerer Points then to Spell Slots. The Slimefolk can then short rest to gain more Warlock Spell Slots via Pact Magic, repeating this cycle.
Normally this can be contained because eventually a player either becomes exhausted or is forced to take a long rest. All other races sleep once a day to avoid exhaustion, except Elves who mediate for 4 hours and gain the effects of 8 hours of sleep.
A Slimefolk could stay up for days, weeks, months, years, accumulating god knows how many Spell Slots.
This may not seem like a big deal because you won't let your Slimefolk do this, but what are you going to do when the party wants to take a long rest? The Slimefolk will inevitably opt to take 8x short rests. Once the rest of the party has finished their long rest the a Slimefolk with Sorcerer 2/Warlock 1 would have 11 level 1 Spell Slots.
I suggest the Slimefolk needs an equivalent mechanic to the Elf's Trance, forcing them to take a Long Rest once per day. Here is my suggestion:
Ooze Nature
Your creature type is both humanoid and ooze.
You also don't need to sleep, and don't suffer exhaustion from lack of rest. However maintaining a form for a long period can cause exhaustion, so for 4 hours per day you must return to being an immobile puddle of goo. After, you gain the same benefit as a human does from 8 hours of sleep and when you finish resting you can choose a permanent form as if you were the target of the Alter Self spell.
The wording could use some work, but I'm sure you see the intent.
Best Answer
No. You have a race and its attendant traits, but present as a different race.
You have emphasized the relevant text. You have a race, so you use those traits, but you imitate another race, and don't use those traits.
It should be obvious that your player character is a member of some race: this is step 1 of character creation in the Player's Handbook. Further, this is assumed when the feature uses the phrase true form. The doppleganger character secret explains that you are imitating another race but don't have any of the racial traits of that race, so naturally, you retain the racial traits of your true form.
I'll use an example to explain the feature description.
I am Jimothy, a lawful-neutral Halfling barbarian with the Far Traveller background. This is what the other characters at the table know my character to be.
The secret is this: I am actually a Goliath. My character sheet would read like a Lawful-Neutral Goliath Barbarian Far Traveller, but I present to the party as a Lawful-Neutral Halfling Barbarian Far Traveller.
Note, it seems quite clear that this secret is not intended to use the Doppelganger monster stat block in any way. If it was, it would say so using the convention described in the intro:
The secret name is stylized identically to other secret names, and the word "doppelganger" appears only in the name of the secret, never in its description.