Shevach is commonly translated as praise. However, we also say that Hallel is praise, so there must be something different about it , than the common understanding of praise.
Additionally , in our prayers we find this “word” used many times , and in each world of prayer, with a sense of obligation, or our duty to be ones that practice in being Mishabeach Hashem. Therefore it is an important concept to understand what it means. We find the word in each level of prayer. *Shevach and the different levels of Creation:
Perhaps we can begin to gain an understanding of what is being asked of us in seeing the different translations and contexts offered for Shevach in Torah.
The Malbim describes the process of “shevach” as:
“going beyond”, or the process of elevating and lifting up.  He uses the description Yaakov gave Reuven in his brachos of “יֶ֥תֶר שְׂאֵ֖ת”, superiority in Kehuna. Rashi connects this to the process of the Kohanim who raise their hands when giving the brachos, by נשיאות כפים.
He also describes this elevation as something that you now see as higher, or more than previously , כי יתעלה בעיניהם יותר על מה שהיה מקודם. He says one can find more and more , when one studies the nature of the world, and will find things that were not previously seen, and one will come to recognize the wonders and the wisdom in Hashem’s creations, which was previously hidden.
It is used to describe a person who expands on his “vidui” or confession is considered “Mishubach”
There is a concept of beginning with “disgrace” and to conclude with “glory” (shevach).
The G’marra considers the disgrace that we began as “slaves” or “idol worshipers” and then we were taken out of that status.
Mishneh Torah, Reading the Shema 1:4
When Yisroel (Yaakov Avinu) said in response to his sons saying the Shema , with the words “Baruch Shem Kivod Malchuso L’olam Vaed” it was considered an act of Shevach and we continue with the shevach by saying those words when we daven. 
Shevach- as Humbling oneself
There are a few verses in Tehillim and Koheles that also describe “Shevach” as humbling oneself to be more.
Shevach– Harav Simcha L. Weinberg, n”y
Harav Simcha Weinberg, n”y defines Shevach as Profitable. Profit as something that grows.
I think it can be concluded from all these different examples that “Shevach” is a process of elevation, of lifting up, of processing the world until it is enhanced and superior to that which was prior. It is therefore not simply a “Praise” of Hashem.
When Adam Harishon saw what was possible with Teshuva, when seeing how Kayin was guilty of murder yet still was able to do Teshuva, finding something that which he had not seen before, he immediately composed Mizmor Shir L’yom Hashabas as an act of Shevach to Hashem..
It also can be an internal discovery of the superiority, of the elevated Neshama within ourselves as described by Rashi with Reuven to better serve Hashem.
May we all be Zoche to master the Avodah of Shevach so that our very Tefillah is Shevach and may we keep discovering more and more about Hashem’s ways and find more and more ways to use and raise Shevach to Hashem.
אֵין מוֹצִיאִין לַאֲכִילַת פֵּרוֹת וּלְשֶׁבַח קַרְקָעוֹת וְלִמְזוֹן הָאִשָּׁה וְהַבָּנוֹת מִנְּכָסִים מְשֻׁעְבָּדִים, מִפְּנֵי תִקּוּן הָעוֹלָם. וְהַמּוֹצֵא מְצִיאָה, לֹא יִשָּׁבַע, מִפְּנֵי תִקּוּן הָעוֹלָם: The court does not appropriate liened property that has been sold to a third party for the consumption of produce or for the enhanced value of land
 וְכָל הַמַּרְבֶּה לְהִתְוַדּוֹת וּמַאֲרִיךְ בְּעִנְיָן זֶה הֲרֵי זֶה מְשֻׁבָּח. whosoever elaborates in confessing and extends this subject is, indeed, praise-worthy.
 מַתְחִיל בִּגְנוּת וּמְסַיֵּים בְּשֶׁבַח. מַאי בִּגְנוּת? רַב אָמַר: ״מִתְּחִלָּה עוֹבְדֵי עֲבוֹדָה זָרָה הָיוּ אֲבוֹתֵינוּ״. [וּשְׁמוּאֵל] אָמַר: ״עֲבָדִים הָיִינוּ״. It was taught in the mishna that the father begins his answer with disgrace and concludes with glory. The Gemara asks: What is the meaning of the term: With disgrace? Rav said that one should begin by saying: At first our forefathers were idol worshippers, before concluding with words of glory. And Shmuel said: The disgrace with which one should begin his answer is: We were slaves.
 כְּלוֹמַר שְׁמַע מִמֶּנּוּ אָבִינוּ יִשְׂרָאֵל יְיָ׳ אֱלֹהֵינוּ יְיָ׳ פָּתַח הַזָּקֵן וְאָמַר בָּרוּךְ שֵׁם כְּבוֹד מַלְכוּתוֹ לְעוֹלָם וָעֶד. לְפִיכָךְ נָהֲגוּ כָּל יִשְׂרָאֵל לוֹמַר שֶׁבַח שֶׁשִּׁבֵּחַ בּוֹ יִשְׂרָאֵל הַזָּקֵן אַחַר פָּסוּק זֶהThis means, “Our father, Israel, hear this, our [confession of faith]: ‘the Lord our God is one Lord'”. The aged patriarch then ejaculated, “Blessed be the name of His glorious Sovereignty for ever and ever.” Hence, all Israelites keep the custom of reciting, after the first verse of the Shema, the thanksgiving uttered by the Patriarch Israel. (Sefaria)
 Prayer is divided according to the different levels of creation.
The world of “Asiah”
לְעוֹלָם יְהֵא אָדָם יְרֵא שָׁמַֽיִם בַּסֵּֽתֶר וּבַגָּלוּי- A person should always be in awe of God, privately as well as openly, …לְפִיכָךְ אֲנַֽחְנוּ חַיָּבִים לְהוֹדוֹת לְךָ וּלְשַׁבֵּחֲךָ וּלְפָאֶרְךָ וּלְבָרֵךְ וּלְקַדֵּשׁ וְלִתֵּן שֶֽׁבַח וְהוֹדָיָה לִשְׁמֶֽךָ- Therefore, we are obligated to thank You, to praise You, and to glorify You; to bless, to sanctify, and to offer praise and thanks to Your Name.
The world of “Yetzirah”
יִשְׁתַּבַּח שִׁמְךָ לָעַד מַלְכֵּֽנוּ הָאֵל הַמֶּֽלֶךְ הַגָּדוֹל וְהַקָּדוֹשׁ בַּשָּׁמַֽיִם וּבָאָֽרֶץ- Praised be Your Name forever,our King, Almighty the great and holy King in heaven You will be praised in heaven as well as on earth.
The world of “Briah”
הַמֶּֽלֶךְ הַמְּ֒רוֹמָם לְבַדּוֹ מֵאָז, הַמְּ֒שֻׁבָּח וְהַמְּ֒פֹאָר וְהַמִּתְנַשֵּׂא מִימוֹת עוֹלָם- The King Who is praised and glorified and uplifted, from the beginning of time.
תִּתְבָּרֵךְ ה׳ אֱלֹקינוּ בַּשָּׁמַֽיִם מִמַּֽעַל וְעַל הַאָֽרֶץ מִתָּֽחַת עַל כָּל שֶֽׁבַח מַעֲשֵׂה יָדֶֽיךָ וְעַל מְאֽוֹרֵי אוֹר שֶׁעָשִֽׂיתָ הֵֽמָּה יְפָאֲרֽוּךָ סֶּֽלָה -Be Blessed, Hashem, our Empowerer, in the heavens above and on earth below for the excellent works of Your hands and for the light-giving luminaries which You formed; they will glorify You forever.
וְכֻלָּם פּוֹתְ֒חִים אֶת פִּיהֶם בִּקְדֻשָּׁה וּבְטָהֳרָה בְּשִׁירָה וּבְזִמְרָה וּמְבָרְ֒כִין וּמְשַׁבְּ֒חִין וּמְפָאֲרִין וּמַעֲרִיצִין וּמַקְדִּישִׁין וּמַמְלִיכִין -And they all open their mouths in holiness and purity, with song and music, and they bless, and praise, and glorify, and revere, and sanctify, and proclaim the sovereignty of—
וְהָאוֹפַנִּים וְחַיּוֹת הַקֹּֽדֶשׁ בְּרַֽעַשׁ גָּדוֹל מִתְנַשְּׂ֒אִים לְעֻמַּת שְׂרָפִים לְעֻמָּתָם מְשַׁבְּ֒חִים וְאוֹמְ֒רִים And the Ofanim, Chayos haKodesh, and the holy Chayos, with a mighty sound rise toward the Serafim. Facing them, they offer praise and say.