From what I have noticed in these forums, it can happen either way eligibility first followed by background or other way around BG first. For CEC and FSW I feel eligibility is more common to be closed as the last item, less likelier that eli closes before BG. It is the other way around for PNPs though where eligibility get be faster before BG, the VO who usually process PNP i.e. Sydney / Ottawa might be following that patter I guess.
In your case Security and criminality have passed is good sign that you file might close soon.
I assume you got to know from GCMS notes that the IRCC analyst has noted as "Not able to verify Canadian employer online presence" and yes it is waiting for an officer to approve or reject.
Giving T4, pay stubs or even bank statements shows you have worked, but I feel doesn't clear lack of online presence for employer.
- Does your company have a website? Are they a public lister firm, do they have shareholders reports etc... Which you can download that report and give to IRCC, along with hyperlink to their website in a webform?
If your is not a public company, please ask your employer to provide you will the set of PDF files they describe themselves their business, their leadership, photos of their offices, list of products / services, Business Numbers (BN) etc.. They might be using a set of files like this when they apply for WPs for their employees. try giving all those, any other public corporate marketing material in a webform too.