Is 1 Corinthians 7:26–40 not the 'Word of God'?

I would suggest "authority". Early Christians recognise his authority. I see here in 1 Cor 7 Paul put up a counsel.

Php 4:8 NIV Finally, brothers and sisters, whatever is true, whatever is noble, whatever is right, whatever is pure, whatever is lovely, whatever is admirable--if anything is excellent or praiseworthy--think about such things.

Whatever is right? Love/care. Paul's writing demonstrates his "heart": 1Cor7:32 I would like you to be free from concern. v35: I am saying this for your own good, not to restrict you, but that you may live in a right way in undivided devotion to the Lord.

He is suggesting something good, it is up to the reader to evaluate considering also their own situation. Php 4:8 again says "think". To me, Paul's opinion/counsel is not that different from Jesus saying in Matthew 19:10-12.

Using the basic rules that Biblical Literalists use when determining what is to be taken as "literally the Word of God", we find the basic principle:

When the plain sense of Scripture makes common sense,seek no other sense;

Therefore, take every word at its primary, ordinary, usual, literal meaning unless the facts of the immediate context, studied in the light of related passages and axiomatic and fundamental truths indicate clearly otherwise.

That makes things pretty simple. In context, this was an Epistle, which is to day, a letter of instruction to the Church at Corinth. Literally, Paul is saying that this is something he is speaking "with permission" - that is, the author himself is stating that this is his personal position, not something that the Holy Spirit guided him to write.

Therefore, it is reasonable to believe and understand that these words were not laid upon Paul by the Holy Spirit, but "by permission" indicates that he had the Holy Spirit's permission to write these things. That implies he sought out the will of God in these things and found no opposition or reason not to write these things.

This means, logically, that these verses are not the direct inspiration of the Holy Spirit, but are not in contradiction to the will of God.

This is all in line with the Jamieson-Fausset-Brown Bible Commentary

25. no commandment of the Lord: yet . my judgment-I have no express revelation from the Lord commanding it, but I give my judgment (opinion); namely, under the ordinary inspiration which accompanied the apostles in all their canonical writings (compare 1Co 7:40; 1Co 14:37; 1Th 4:15). The Lord inspires me in this case to give you only a recommendation, which you are free to adopt or reject-not a positive command. In the second case (1Co 7:10, 11) it was a positive command; for the Lord had already made known His will (Mal 2:14, 15; Mt 5:31, 32). In the third case (1Co 7:12), the Old Testament commandment of God to put away strange wives (Ezr 10:3), Paul by the Spirit revokes.

Then again, Clarke's commentary states:

I have no commandment of the Lord - There is nothing in the sacred writings that directly touches this point.

Yet I give my judgment - As every way equal to such commandments had there been any, seeing I have received the teaching of his own Spirit, and have obtained mercy of the Lord to be faithful to this heavenly gift, so that it abides with me to lead me into all truth. In this way I think the apostle's words may be safely understood.

Which, of course, would indicate that this is the direct inspiration of the Holy Spirit, which leaves the concept of a fully inspired Scripture intact.

So apparently the answer to the question is, not surprisingly, "There seems to be more than one point of view on the subject, neither authoritative."

As a sige point, this isn't the only place in 1 Corinthians where such a statement is made. Verse 6 has a similar statement (KJV):

But I speak this by permission, and not of commandment.

which most commentaries interpret to be referring to the preceding verse, but again, interpret differently.

Paul is not trying to make the point that 1 Corinthians 7:12ff is his opinion where the rest is God's inspired Word. Rather, Paul knows the oral tradition of Jesus’ sayings on divorce that were later written down in the Gospels, but he is not aware of a time when Jesus ever spoke specifically to a situation in which one spouse becomes a Christian and the other remains unconverted. Therefore, he carefully distinguishes between the written words of Jesus as recorded in the Gospels and his own understanding of how Jesus’ teaching would apply to this new situation. Paul makes the notations (“Not I, but the Lord” and “I, not the Lord”) in order to delineate between directly quoting Jesus and not quoting Jesus.

So, Paul is not saying that 1 Corinthians 7:12ff is simply his wisdom or opinion. Paul is saying that 1 Corinthians 7:12 and following is newly revealed Scripture, led by the Spirit, through his pen. When Paul says, “Not I, but the Lord”, he is saying this is a quote directly from the Lord, recorded in Matthew 5:32. When Paul says, “I, not the Lord”, he is saying this is a new word revealed through him from God in the Holy Spirit.

Simply put, Paul is delineating between quoting Jesus and not quoting Jesus.

Paul views his admonition here as authoritative and inspired, not merely as human wisdom (v. 40; cf. 14:37–38).