Did Paul refer to James as a literal brother of Jesus?

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Christ mythicists claim that Paul refers to James as a brother of the Lord only in the same sense that all Christians are (spiritual) brothers.

Here are the relevant passages (NRSV):

Galatians 1:19 Then after three years I did go up to Jerusalem to visit Cephas and stayed with him fifteen days; but I did not see any other apostle except James the Lord’s brother.

1 Corinthians 9:5 Do we not have the right to be accompanied by a believing wife, as do the other apostles and the brothers of the Lord and Cephas?

There are no applicable translation notes in the NET.

Here is an example of Christ mythicist Richard Carrier making the aforementioned argument:

I argued that all Christians were brothers of the Lord because: (a) they were all adopted sons of God, (b) Jesus was an adopted son of God, and (c) that by definition made them all the adopted brothers of Jesus; and (d) Christians called each other brother, therefore they would have called each other brothers of Jesus, too. I also showed (e) that they believed Jesus had explicitly called them his brothers and (f) they explicitly said Jesus was only the firstborn among many brethren. Another important point I made is that Jesus became Lord at his adoption, so Christians would be brothers of the Lord specifically, a uniquely Christian concept (and one that could only have been uttered after the origins of Christianity; e.g., even if James was the biological brother of Jesus, he would never have been called the brother of the Lord until Christians invented that phrase for him).

On the other hand, Reddit user Christosgnosis says:

The Greek grammar is specifically fraternal – not language that would denote a spiritual brother as Paul says that differently using other Greek grammar when he means spiritual brother – just reciting the scholarship on this.

So what’s the deal? Is it linguistically conclusive whether Paul referenced James as having a literal familial relation to Jesus versus being merely a spiritual brother?

I know this may seem like a strange question, and it may be tempting to cite external historical evidence, but please keep your answers confined to linguistic evidence regarding how Paul used (or would have used) the relevant terms. Christ mythicists are aware of the Gospels and Josephus, for example, but they reject their veracity for various reasons.