I plan to delete the Google Search Console property for my website. What are the consequences of doing so?
If you delete the property from search Console. You will lose all the past search performance data (from which Keyword, you are getting how much impression, your SERP Rankings etc).
Apart from that, you will lose the international targeting (if you have set, that you want to target specific country), after deleting it will universal.
You will lose control over your site's sitemap contribution from your side to Google. You won't able to tell Google, which page you need to index, google will decide.
You will lose control to set Sitelinks for your website, which appears in Google search engine when someone search your brand name.
You won't be able to remove any url of your site from google, if you want.
Overall, you will be breaking the bridge between your site and Google.