In a previous article, I told you which stack I'm using for outreach purposes. It includes Mailshake, which is connected to a personal Gmail account for outreach purposes, via the official API.
It's great but you have to be aware of Gmail limits, which can even be stricter than the ones usually advertised.
Depending on which article you'll come across, you'll read that the limit would be 200 or 500 emails per day per Gmail account but I strongly advise against sending simultaneous mass emails via Gmail, even if the total doesn't exceed 200 per day. I had a new account suspended for 24 hours just for 38 emails sent at the same time.
So if you import a large list (like a curation of your Linkedin contacts), make sure you set the advanced settings of Mailshake (when importing a list) so that the platform sends your emails in very small batches, e.g. 3 or 4 emails every 10 or 15 minutes. It will take longer to reach all recipients but it will prevent an account suspension (for 24h) or even an account deletion, which does happen.
One more thing: never ever use your main legacy Gmail account for outreach purposes, because you never know what could affect it, especially when it's connected to a whole range of other services (Google Documents, Analytics, etc.). If you respect these rules, you'll never have unpleasant surprises caused by Gmail limits.