"Chapter 1—God's Purpose in the Church It is God's purpose to manifest through His people the principles of His kingdom. That in life and character they may reveal these principles, He desires to separate them from the customs, habits, and practices of the world. He seeks to bring them near to Himself, that He may make known to them His will. 6T 9"
"But ye are a chosen generation, a royal priesthood, an holy nation, a peculiar people; that ye should shew forth the praises of him who hath called you out of darkness into his marvellous light:"
Both passages discuss God's purpose for His people to be distinct from the world and to reveal His principles/praises. The idea of separation and manifestation of God's character connects them thematically.
"This was His purpose in the deliverance of Israel from Egypt. At the burning bush Moses received from God the message for the king of Egypt: “Let My people go, that they may serve Me.” Exodus 7:16 . With a mighty hand and an outstretched arm God brought out the Hebrew host from the land of bondage. Wonderful was the deliverance He wrought for them, punishing their enemies, who refused to listen to His word, with total destruction. 6T 9.2"
"And thou shalt say unto him, The Lord God of the Hebrews hath sent me unto thee, saying, Let my people go, that they may serve me in the wilderness: and, behold, hitherto thou wouldest not hear."
EGW directly quotes Exodus 7:16.
"God desired to take His people apart from the world and prepare them to receive His word. From Egypt He led them to Mount Sinai, where He revealed to them His glory. Here was nothing to attract their senses or divert their minds from God; and as the vast multitude looked at the lofty mountains towering above them, they could realize their own nothingness in the sight of God. Beside these rocks, immovable except by the power of the divine will, God communicated with men. And that His word might ever be clear and distinct in their minds, He proclaimed amid thunder and lightning and with terrible majesty the law which He had given in Eden and which was the transcript of His character. And the words were written on tables of stone by the finger of God. Thus the will of the infinite God was revealed to a people who were called to make known to every nation, kindred, and tongue the principles of His government in heaven and in earth. 6T 9.3"
"Now therefore, if ye will obey my voice indeed, and keep my covenant, then ye shall be a peculiar treasure unto me above all people: for all the earth is mine: And ye shall be unto me a kingdom of priests, and an holy nation. These are the words which thou shalt speak unto the children of Israel."
Both passages discuss God's desire for Israel to be a special people, set apart to obey Him and reveal His character/government to the world. The connection lies in the purpose and calling of Israel.