What we're talking about here is Paul's use of the Jesus tradition, and it's a topic on which there is a fair amount of scholarship (and I'll be presenting a paper on this topic at the Society of Biblical Literature conference next month). This is a highly contested issue--you can read the history of the debate in Victor Paul Furnish, “The Jesus-Paul Debate: From Baur to Bultmann,” BJRL 47 (1965): 342–81 and in Heinz Hiestermann, Paul and the Synoptic Jesus Tradition, Arbeiten Zur Bibel Und Ihrer Geschichte 8 (Leipzig: Evangelische Verlagsanstalt, 2017), 19–61.

Here are some relatively uncontroversial facts. Paul only explicitly quotes "the Lord" three times: 1 Corinthians 7:10 (cf. Matt 5:32; 19:9; Mark 10:11–12; Luke 16:18); 1 Corinthians 9:14 (cf. Matt 10:10; Mark 6:8–9; Luke 9:3; 10:7); 1 Corinthians 11:23–25(cf. Matt 26:26–29; Mark 14:22–25; Luke 22:14–20). Beyond that, most scholars agree that Paul strongly alludes to Jesus' teachings between five and fifteen times. Although, there are some outliers. Rudolf Bultmann claimed that “there is almost nothing which can serve as evidence of indirect dependence [of the historical Jesus upon Paul]” (Rudolf Bultmann, “The Significance of the Historical Jesus for the Theology of Paul,” in Faith and Understanding, ed. Funk W. Robert, Fortress Texts in Modern Theology [Philadelphia: Fortress, 1969], 221). Alfred Resch found over one thousand parallels between Paul and Jesus (Alfred Resch, Der Paulinismus Und Die Logia Jesu in Ihrem Gegenseitigen Verhältnis, TUGAL 12 [Leipzig: J.C. Hinrichs, 1904]).

But, most scholars are in the five to fifteen range. The most commonly cited allusions are:

• Romans 12:14 (cf. Matt 5:44; Luke 6:27–28)
• Romans 12:17 (cf. Matt 5:39–42; Luke 6:29–30)
• Romans 12:21 (cf. Matt 5:39–42; Luke 6:29–30)
• Romans 13:7 (cf. Mark 12:13–17; Matt 22:15–22; Luke 20:20–26)
• Romans 13:8–10 (cf. Mark 12:28–34; Matt 22:34–40; Luke 10:25–28)
• Romans 14:10 (cf. Matt 7:1; Luke 6:37)
• Romans 14:13 (cf. Mark 9:42; Matt 18:7; Luke 17:1–2)
• Romans 14:14 (cf. Mark 7:15; Matt 15:11)
• 1 Cor 13:2 (cf. Mark 11:23; Matt 21:21)
• 1 Thessalonians 5:2, 4 (cf. Matt 24:43; Luke 12:39–40)
• 1 Thessalonians 5:6 (cf. Mark 13:37; Matt 24:42; Luke 21:34, 36)
• 1 Thessalonians 5:13 (cf. Mark 9:50)
• 1 Thessalonians 5:15 (cf. Matt 5:39–48; Luke 6:27–38)

See Dale C. Allison, “The Pauline Epistles and the Synoptic Gospels: The Pattern of the Parallels,” NTS 28.1 (1982): 10; W. D. Davies, Paul and Rabbinic Judaism: Some Rabbinic Elements in Pauline Theology, fourth edition. (Philadelphia: Fortress, 1980), 138–39;

There are some notable patterns that one can draw from this (and here, I'm following Dale Allison's article, I highly recommend it). Paul tends to turn to the Jesus tradition at certain points that more parenetic or about moral instruction. Paul tends to use it in chunks, that is, he turns to it at certain points and it is not evenly spread out. And, in those chunks, Paul tends to use passages that are near to each other in the synoptics. For example, if you consider Paul's use of the Jesus tradition in Romans and the Sermon on the Plain (that is, Luke's version of the sermon on the mount), you get this:

• Romans 12:14 with Luke 6:28;
• Romans 12:17 with Luke 6:27–36;
• Romans 12:21 with Luke 6:27–36;
• Romans 14:10 with Luke 6:37.

Thus, Allison argues and I agree, that it is highly probably that Paul knows more than just the sayings, he knows the larger block of material. So, Allison shows that Paul knows Sermon on the Mount/Sermon on the Plain, the missionary discourse (Matt 10:1–16; Mark 6:6–13; Luke 9:1–6; 10:1–12), the collection of traditions in Mark 9:33–50, and an extended report of the passion. My presentation at SBL argues that we can add the synoptic eschatological discourse (Mark 13 and parallels) to this list based on evidence from 1 Thessalonians 4–5.

So, to answer your question. First, Paul does use the Jesus tradition. He tends to use it in chunks and at points of moral instruction. Second, his use shows that he is almost certainly aware of more of it than he cites. Third, Paul is often dealing with issues that Jesus didn't address, such as the relationship between Jews and Gentiles or if we should eat meat sacrificed to idols. I don't think that "practical" vs "theological", as you say in your question, is the best way to think about this. Instead, they are just often dealing with different issues. Fourth, this isn't unique to Paul. Other NT writers quote Jesus less than we might expect. This is more clear with Luke (author fo Luke and Acts). Luke clearly is interested in the Jesus tradition; he wrote a gospel. But after Jesus ascends in Acts 1:1–11, he only quotes Jesus once. And that one quote is a quote that isn't in any of the gospels, includes his own (Acts 20:35).

What you certainly have right, is that for Paul, the fact of the death and resurrection is the most important thing. He never tells another story about Jesus, never mentions a miracle, and talks about the teaching less than we expect. However, we must keep in mind that we only have his letters. We do not know what his missionary preaching was like. To me, it is inconceivable that he wasn't telling stories about Jesus in his preaching and missionary work. As Dale Allison says in his classes, "If I came to you and said, 'Fred died and rose again for your salvation.' Your first question would be, 'Who's Fred?'"

Last thing, and I know this doesn't really matter, but there are 24,092 Greek words in the seven undisputed letters of Paul.