WeiWeiMan is definitely correct. Essentially, the ATAR has a number of characteristics that determine its significance. First, the ATAR is a rank, not a mark (i.e. a relative measure rather than an absolute measure). Its sole purpose is to determine your position compared to other students who completed their HSC in your year, and this information is used by universities and other institutions in determining whether to make offers to applicants. Once a student receives an offer to study a particular degree (especially if it is their dream course), the ATAR no longer bears much significance, except where a student may wish to transfer to a different degree/university, in which case their ATAR can still be relevant.
While a student's ATAR does provide an indication of their academic capability, this is because it is informed by the student's HSC results. For example, a 95 ATAR generally indicates that a student achieved favourable HSC marks across their subjects. With that being said, a student's ATAR may not necessarily define whether they end up being successful. There have been multiple cases of students with lower ATARs who managed to become successful beyond the HSC, and students with higher ATARs who have struggled in maintaining such standards beyond the HSC.
Of course, just because the ATAR is a rank does not mean that it should be dismissed. Students are still encouraged to do their utmost in order to maximise their ATAR, as gaining entry into their desired course (in the case of most degrees) that way would be less demanding than having to pursue alternative and potentially longer pathways, should they not succeed in receiving an ATAR-based offer. On that note, an 85+ ATAR does provide a rather wide range of options (including at USyd and UNSW), although it is important to keep in mind that there are degrees with higher ATAR requirements that may be inaccessible with an ATAR in the 85+ range. These extend beyond a Bachelor of Laws and a Doctor of Medicine, and are certainly not unique to USyd and UNSW.
The specific university that a student attends typically matters in fields such as law, where the university that graduates have attended is taken into consideration, in addition to more conventional elements such as academic performance and relevant work experience. However, this is not applicable to most other fields, where only the more conventional elements are considered.
I hope this helps!