Crm with shared inbox and time tracking

Hello, my company is searching for a CRM that allows to manage leads and contacts with the possibility to track everything (calls, emails, notes) and have everything stored in the contact or deal page. One of the most important things is that you should be able to connect both your personal email and the shared inbox of the company (eg. support@mail.com) so everybody can respond to the ticket, assign the email, comment with the colleagues. You should be able to see if some colleague is already responding to that mail in order to avoid a double response to that email. If there is an addon for Gmail it would be best, so you can create leads directly from your personal GMail. Another important thing is to be able to see the day and organize your tasks in a way that I can see how much time I dedicated to lead conversion, if I spent too much time in calls (for this reason one should be able to note the calls and the duration/result of the call). Also a report to see how many times the employees spend in time conversion, in calls, in order to have a comparison between them. I already tried the most important ones like Salesforce Essentials and Pipedrive, but the only ones that come close to our needs are ZohoCRM with TeamInbox addon (but the reports are a bit too difficult to analyze and create, and TeamInbox doesn't sync the read status of the email so all emails in GMail are still unread), and Hubspot (but we don't need the marketing side) but it has some flaws. Already tried espoCRM but it doesn't have any GMail addon and the shared inbox is very poor.

Do you have any other suggestion? The budget is around 30€/user/month.

Thanks