Why does the Haggadah interpret ביד חזקה (strong hand) as referring to the plague of דבר (pestilence)? Why don’t the other plagues demonstrate a strong hand?
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Each plague was done with a finger of Hashem, as it says "אצבע אלקים היא" (Shemos 8:15) by כנים, and דבר was the fifth plague, making it 5 fingers, a full hand.
(my) Source: Maaseh Nisim Hagada by Rabbeinu Yaakov m'Lisa (aka the Nesivos Hamishpat) quoting "the commentaries"
While I was looking back through my Haggadas for the source, I found this as well:
The Haggada attributed to the Malbim quotes a Medrash (Shemos Rabba 10:2) that with every plague that came upon Mitzrayim, there was an accompaniment of דבר. Therefore this plague was inclusive of all the plagues, and is more than just a "finger" like the other plagues.
Of interest is Shemot Rabbah 10:1, which quotes R' Yehoshua ben Levi's teaching that each of the 10 plagues came with a side-plague of Pestilence.
While looking for that source I came across this on vbm-torah.org, which brings multiple answers to your question.
It was suggested that this was the Egyptians first encounter with a plague that’s objective was to bring about death. It demonstrated Hashem’s ability to bring about life and death.
(I will try and locate the Rishon that said this.)