QB Issue Resolution:

Nope. You at worst might have trouble directly opening your 2013 file in 2019 so I always suggest using a backup copy of old and restore into new. 6 years jump it would be better if you had access to a licensed copy of 2016 (friend, your CPA, etc.)

Resolution for Issue 'I want to replace QB Pro 2013 with QB Pro 2019 with Enhanced Payroll. Are there any compatibility issues I need to be aware of?' available: Yes (Solved).
Source: Intuit Community forum.

I want to replace QB Pro 2013 with QB Pro 2019 with Enhanced Payroll. Are there any compatibility issues I need to be aware of?: this issue or error code is a known issue in Quickbooks Online (QBO) and/or Quickbooks. Support for this issue is available either by self-service or paid support options. Experts are available to resolve your Quickbooks issue to ensure minimal downtime and continue running your business. First try to resolve the issue yourself by looking for a resolution described below. If it is a complex issue or you are unable to solve the issue, you may contact us by clicking here or by using other support options.

Support for Enhanced payroll
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Error Recovery for Enhanced payroll [Canada]
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