Regarding filtering on partial matches, that is already the case. See example below, which shows results of sentences containg 'The' or 'These':
library(tidyverse)
df <- tibble(sentences = head(sentences, 10))
## keep any sentences which do have a partial match of the word 'The'
df %>% filter(str_detect(sentences, "The"))
#> # A tibble: 5 x 1
#> sentences
#> <chr>
#> 1 The birch canoe slid on the smooth planks.
#> 2 These days a chicken leg is a rare dish.
#> 3 The juice of lemons makes fine punch.
#> 4 The box was thrown beside the parked truck.
#> 5 The hogs were fed chopped corn and garbage.
Created on 2021-02-02 by the reprex package (v1.0.0)
If you want to find the exact word (use \\b) but non-case sensitive (use str_to_lower()) then it might look like this:
library(tidyverse)
df <- tibble(sentences = head(sentences, 10))
## keep any sentences which contain both upper/lower case word 'the' exactly
df %>% filter(str_detect(str_to_lower(sentences), "the\\b"))
#> # A tibble: 6 x 1
#> sentences
#> <chr>
#> 1 The birch canoe slid on the smooth planks.
#> 2 Glue the sheet to the dark blue background.
#> 3 It's easy to tell the depth of a well.
#> 4 The juice of lemons makes fine punch.
#> 5 The box was thrown beside the parked truck.
#> 6 The hogs were fed chopped corn and garbage.
Created on 2021-02-02 by the reprex package (v1.0.0)
There are other ways of achieving this, so I won't be afraid that more questions will arise, especially when you get the taste of using the power of regex 
Regex can be quit daunting on how to use it correctly - at least, for me that will always be the case - and for that reason I make use of the RStudio addin RegExplain. For a quick and comprehensive overview of this addin, I hihgly recommend to visit first the RegExplain site.
Note also that RStudio offers several handy cheatsheets under the Help menu and you'll find more (including one for regex) under Browse Cheatsheets.