Generally: a license for software tells you what permissions you have in using and distributing said software. If you produce a piece of software that incorporates other software, you have to look at the license of that software and see whether you are willing to fulfill the conditions as written down in the license. The conditions will make a distinction between you using it for yourself and you incorporating the source code in order to write and distribute your own software. The latter case is interesting, as the use of 3rd-party libraries or source code like from frame works means you have to comply with the license of these when you distribute your software.
In open source one usually distinguishes two type of licenses: the permissive licenses (like MIT, BSD, Apache,...) and the strong copyleft (like GPL). And for libraries there's somewhat a 3rd kind, strong copyleft with linking exception (like LGPL).
The gist of the permissive licenses is that one can make use of the source code on the condition to keep and notify about the copyright without obligation to make the sources public.
The gist of the strong copyleft licenses is that you can only make use of this software when you apply the exactly same conditions, thus usually make use of the very same license for your own software. It usually implies that you have to make source code available.
The gist of the strong copyleft with linking exception is that you can make use of the library without publishing the sources of your software, if you do not modify the library. The need to make sources public only applies when making modifications to the library itself. Often there are other conditions like you need to allow users to replace the library with a functionally equivalent one.
The mentioned frameworks Vue, React and Next JS are all under the MIT license. MIT is a permissive license. So anyone is free to make use of that source code in whatever project - on the condition that the recipients of the software are informed about the use of the framework and its license, thus an appropriate copyright is given in a reasonable place. For Vue it reads:
The MIT License (MIT)
Copyright (c) 2013-present, Yuxi (Evan) You
Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions.
The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
So yes, it's totally fine to use these frameworks (Vue, React, Next JS) in proprietary software if you fulfill this one condition.
Mind though, a permissive license may not apply for every framework. E.g. for Qt the situation looks quite different. Thus always look at the license of source code and libraries you use when you develop. And don't use those where you don't intend to fulfill the conditions.