As you can readily see from numerous posts above, your eCas will ordinarily show when your PR card application is in process within ROUGHLY a week, two at most, of the day when the application and file are opened UNLESS it is being returned to the PR (such as, if it is incomplete, or the fees have not been paid). This will be the ONLY reliable indication of when YOUR PRC application is in process.
Given the changes in how IRCC is reporting timelines, just implemented a bit more than two months ago, it is very likely the automated message system is not kept current and to the extent it is updated it is not likely there is a RELIABLE schedule, even if there has been a more or less reliable schedule in the recent past.
BUT there is little or no reason this should be frustrating. The situation is clear enough. Any and all such information has long been GENERAL and NOT about any particular applications. If you currently know that IRCC is reporting that it is working on applications received as of June 14, that does NOT necessarily mean it is working on or has even opened all applications received as of June 14, but MOST LIKELY HAS OR SOON WILL be opening files received as of June 14, and from that it is EASY, easy as blueberry pie, to infer it is very likely applications received within a few days or a week after that will MOST LIKELY BE opened within the next TWO to FOUR WEEKS. And that is about as precise as it gets. Anyone claiming to know more precisely than that is blowing smoke.
REMINDER: While routinely processed PRC applications will ordinarily result in a Decision Made roughly around the same time the application is opened (even though date of DM technically might not happen for a few days, a week or so, after the date AOR is noted), to be soon followed by the issuance and mailing of the PRC, many PRC applications are NOT routinely processed . . . so, unless and until the PR sees dates for AOR AND DM in eCas, a PR cannot infer much about when a new PRC will actually be sent to the PR. If the PR has solid reasons for believing the application should be routinely processed (such as a PR who has been settled and living in Canada for well more than THREE years, AND has less than 700 days absence in the relevant five years, AND is waiting on a citizenship application to be processed), it is REASONABLE to forecast a LIKELIHOOD the PRC will be mailed within seven to ten weeks of the processing times being reported by IRCC BUT THIS DEPENDS ON A LOT OF BIG IFS and at times IRCC is simply slower than it has been in the recent past, so the actual processing time can be months longer than the reported timelines. And, nonetheless and in the meantime, all the IRCC information is mere a ROUGH GUIDE as to ranges, and it is imprudent to forecast the timeline specifically for individual PRC applications.