In Pakistan there is no problem with the number bit.
In Germany on the Frankfurt airport they will ask why there numbers are not the same.
But when you have your old passport or a copy with you there is no problem anymore.
If I understand your question correctly, and you wonder about any impact on future visa applications (i.e. after you have your new passport, say in April 2021 in your example), I doubt this would have any effect.
Countries you haven't yet visited/applied a visa for generally won't even know about it.
And even if they have the information, I don't see how ...
It depends on the country you want to obtain a visa from, and the type of visa. Some countries will issue visas that are valid only until the passport expires, others accept visas in expired passports if you have both the old and new passport with you.
If you want to apply for a visa in the period between expiration of the old and issue of the new passport, ...