I suggest that the team identifies with the quality of its output.

Longman
identify with: phrasal verb
1 identify with somebody/something to feel sympathy with someone or be able to share their feelings
Humans can easily identify with the emotional expressions of chimpanzees.
He identified with our distress.
2 identify somebody with something to think that someone is very closely related to or involved with something such as a political group
She has always been identified with the radical left.
3 identify something with somebody/something to think that something is the same as, or closely related to, something else
the attempt to identify crime with poverty and social problems

The Longman examples show how the subject associates themselves - or is associated - with the object. This is appropriate for your team, which associates itself closely with quality. There is no suggestion of hubris or arrogance in this usage, which merely asserts an association without any judgmental overtones.

If you need to communicate the commitment to quality and to focus on the team's actions while not boasting, and having the humility to admit that they may be flawed, you might also write:

our team strives for quality of our output

or

our team aspires to quality in our output

Merriam Webster
strive, intransitive verb
to devote serious effort or energy : Endeavour
strive to finish a project

Cambridge
aspire, intransitive verb
to want something very much or hope to achieve something or be successful

I suggest that the team identifies with the quality of its output.

Longman
identify with: phrasal verb
1 identify with somebody/something to feel sympathy with someone or be able to share their feelings
Humans can easily identify with the emotional expressions of chimpanzees.
He identified with our distress.
2 identify somebody with something to think that someone is very closely related to or involved with something such as a political group
She has always been identified with the radical left.
3 identify something with somebody/something to think that something is the same as, or closely related to, something else
the attempt to identify crime with poverty and social problems

The Longman examples show how the subject associates themselves - or is associated - with the object. This is appropriate for your team, which associates itself closely with quality. There is no suggestion of hubris or arrogance in this usage, which merely asserts an association without any judgmental overtones.

If you need to communicate the commitment to quality and to focus on the team's actions while not boasting, and having the humility to admit that they may be flawed, you might also write:

our team strives for quality of our output

or

our team aspires to quality in our output

Merriam Webster
strive, intransitive verb
to devote serious effort or energy : Endeavour
strive to finish a project

Cambridge
aspire, intransitive verb
to want something very much or hope to achieve something or be successful

And the last thought is that the team is committed to the quality of its output

Cambridge
commit
To promise or give your loyalty, time, or money to a particular principle, person, or plan of action:

I suggest that the team identifies with the quality of its output.

Longman
identify with: phrasal verb
1 identify with somebody/something to feel sympathy with someone or be able to share their feelings
Humans can easily identify with the emotional expressions of chimpanzees.
He identified with our distress.
2 identify somebody with something to think that someone is very closely related to or involved with something such as a political group
She has always been identified with the radical left.
3 identify something with somebody/something to think that something is the same as, or closely related to, something else
the attempt to identify crime with poverty and social problems

The Longman examples show how the subject associates themselves - or is associated - with the object. This is appropriate for your team, which associates itself closely with quality. There is no suggestion of hubris or arrogance in this usage, which merely asserts an association without any judgemental overtones.

I suggest that the team identifies with the quality of its output.

Longman
identify with: phrasal verb
1 identify with somebody/something to feel sympathy with someone or be able to share their feelings
Humans can easily identify with the emotional expressions of chimpanzees.
He identified with our distress.
2 identify somebody with something to think that someone is very closely related to or involved with something such as a political group
She has always been identified with the radical left.
3 identify something with somebody/something to think that something is the same as, or closely related to, something else
the attempt to identify crime with poverty and social problems

The Longman examples show how the subject associates themselves - or is associated - with the object. This is appropriate for your team, which associates itself closely with quality. There is no suggestion of hubris or arrogance in this usage, which merely asserts an association without any judgmental overtones.

If you need to communicate the commitment to quality and to focus on the team's actions while not boasting, and having the humility to admit that they may be flawed, you might also write:

our team strives for quality of our output

or

our team aspires to quality in our output

Merriam Webster
strive, intransitive verb
to devote serious effort or energy : Endeavour
strive to finish a project

Cambridge
aspire, intransitive verb
to want something very much or hope to achieve something or be successful