Butler is the go to automation tool for Trello boards. It does provide a Http Request action to get, post and put for 3rd party services. This can be used interface with CRM APIs.
In addition, I am using a low-code platform which comes with Trello modules and triggers. I write namely in python using py-trello libraries where I needed more complex processing on Trello data. There are http triggers which can be used with CRM webhooks if they are available. This can be also be used for webhooks from Trello.
As for depth of work with Trello, I wrote an Trello Butler add-on with custom Power Ups using the above. Hence depending on what is available on the CRM, there should not be any difficulty in get Trello data to the CRM.
Do note that if the CRM is a Trello Power Up, these are usually closed systems.
As a bonus, the above platform has a CRM package for Salesforce together with other packages such as Google Sheet, gmail, SMTP mail, simple dashboard as a response to web enquiry, form,..etc it is a good tool for exchange of data between a CRM application and Trello.
My proposal is to show you the capabilities that can be deployed to integrating with external systems with data from Trello using a combination of modules, trigger, http request using my custom Butler Add-on application. I have budgeted for 2 man-hours including 1hr online capability demo and 1-hr custom development a API call to a simulate endpoint from within Trello.