Formal version of "stuck in one's old ways" [duplicate]

You can say that the organizations are resistant to change. Here resistance means

The refusal to accept or comply with something

[Oxford Dictionary of English]

I suggest the word hidebound.

adj. "Unwilling or unable to change because of tradition or convention." - Lexico

or "having an inflexible or ultraconservative character." - Merriam-Webster

sclerotic

Becoming rigid and unresponsive; losing the ability to adapt.

‘sclerotic management’

definition from lexico

Some hits in COCA:

France along with many of the other countries in the E.U. have a sclerotic economy that's not producing the jobs

Barack Obama's vision of centralized government, surrounded by a web of sclerotic bureaucracies

You'll also see how far the new director plans to take this sclerotic state institution in the direction of " up and out. "

Seems to fit the bill perfectly.

You could change the structure of the sentence and use the word entrenched:

For the organisations, these ways of operation are very much entrenched.

You could say they are stuck in their old ways but you are looking for less casual terms.

In formal terms they rely on more traditional methods or they could be said to stick with traditional ways. For very formal terms you would substitute sticks to with adheres to but the vocabulary starts to get in the way.

Their ways are from the previous century or ...a bygone age

They have learned nothing of modern ways.

I often feel the same way.