There are other data sources to consider monitoring, too, if you or your SEO expert are using an SEO program management tool, like SEMrush (my recommendation). These tools have significant price differences. In my opinion, the best low-cost one is SEMrush. In the higher-priced range, there are Brightedge, Conductor, and some others that require a significant budget and are great for comprehensive programs. Either way, there are some other KPIs that you can generally report on, as listed here:
Audit score: Audit score is a summary of your total website's SEO health. It's typically a scale of 100. You want to see an audit number of at least 70/100 and have it increase the more you do website fixes as part of your audit.
Errors: Many SEO Agency program tools provide a numerical summary of the total SEO errors a website has. As time goes on, you want to see this number decrease since you are fixing the errors outlined in your audit phase (via Screaming Frog or whatever tool you might use).
Mentions: Brand mentions are traditionally a PR or social media metric but are now proving SEO value. The more often your brand and website are mentioned online tends to result in more traffic and links, so it's important that you monitor if this is on the increase. Ideally, it will be increasing each month.
Referral report (available in Google Analytics or other website analytic tools): This report is critical if you are doing optimizations on other websites outlined in the coming book sections (YouTube, blogs, press releases, Amazon) in the hopes of getting traffic back to your site. Google provides a list of websites where users are clicking from in the Acquisition ➪ All Traffic ➪ Referrals report. Trend how many visits are coming from referring sites and list individual traffic trends from important sites that you're optimizing (for example, YouTube, etc.).
Device or operating system: In Google Analytics, a report is available that provides a list of devices that are driving users to your site. Upon logging in, visit the Audience Mobile Devices report to get an idea of what devices are driving traffic to your site. If a device is not driving traffic, engagement, or conversions, you should consider testing the user experience within the device to see whether there's an issue.
Reporting on these metrics often is important. Typically, I recommend pulling these KPIs into a trended report at least on a monthly basis. I've seen some sites do a report every week or every quarter. It's up to you and your expectations and goals for SEO. The higher the expectations, the higher frequency of reporting you should consider.