No, unless your DM decides otherwise
Even though the teleport ability of the Manifest Echo does not say so explicitly, the Sage Advice Compendium has explicitly ruled that equipment worn or carried is taken along during teleportation:
Misty step doesn’t say the caster can bring worn or carried equipment with them. Are they intended to leave everything, including their clothes, behind?
No, the caster’s worn and carried equipment are intended to go with them.
Some teleportation effects do specify that you teleport with your gear; such specification is an example of a rule being needlessly fastidious, since no teleportation effect in the game assumes that you teleport without your clothes, just as the general movement rules don’t assume that you drop everything when you walk.
Teleportation effects that allow you to transport additional creatures say so, such as the Teleport spell:
This spell instantly transports you and up to eight willing creatures of your choice that you can see within range, [...]
Manifest Echo by itself only teleports you and your equipment. However, here the situation is somewhat different: the passenger creature is not another creature standing next to you, that you can elect to also teleport without extra effort. You have lifted up this creature and are carrying it around, it is not independent of you. The question then is if you can consider a carried creature to be part of your equipment?
Arguments for a creature counting as equipment
The main argument for this comes from the Variant Encumbrance rules on p. 176 of the PHB:
The rules for lifting and carrying are intentionally simple. Here is a variant if you are looking for more detailed rules for determining how a character is hindered by the weight of equipment.
While the rule itself is optional, it treats anything that the character is lifting or carrying as "equipment": the total weight of what you carry is what determines penalties to movement, and this total is referred to here as the "weight of equipment". If creatures you carry would not count against the "weight of equipment", they would not slow your movement speed.
Now, it's possible (even likely) that the writers of the PHB did not think of carrying a creature when they used the term equipment here, because you normally do not carry creatures around, and they instead should have referred to "the weight of everything the character carries."
A secondary argument is that if a character had a small cage with a live canary in their equipment (to detect poison gas in dungeons early), would you rule the canary is left behind when they teleport because as a creature it cannot count towards their equipment?1 I wouldn't, but like a PC, the canary is a creature.
Arguments against a creature counting as equipment
First, when game terms are not defined we use the common English definition of the term, and for equipment or gear that is:
the set of articles or physical resources serving to equip a person or thing: such as (1): the implements used in an operation or activity
which does not sound as if this should include persons. Normally, when you think of equipment, you think of objects you carry around.
Second, the question of the canary falls more into the territory of how to treat harmless, diminutive creatures, namely that one likely best ignores their being creatures in most cases.
Third, the reason why teleporting is limited to an individual or defined number of creatures, is game balance. Taking a PC along with you, wether in a bag or on your shoulder, is a lot more powerful than having a canary in your backpack. Allowing a character to take along a fellow PC by lifting them up temporarily so they become "equipment" is a bit of cheating, it creates a loophole and circumvents the restriction that you can only teleport yourself.
Allowing this would significantly increase the power of these spells and abilities.
I think overall characters are not intended to count as equipment, and hence you will not be able to teleport with a carried creature.
If the DM prefer the rule of cool, and wants to allow heroic shenanigans, like the wizard nearly breaking down to put the barbarian over their shoulder to teleport away with them, or like here, the Echo Knight bagging a fellow character, they can rule otherwise.
1 If you rule that the canary is left behind, Misty Step is a great way to get rid of lice, tapeworms, fleas, and other parasites.