How to convert mixed time formats with strings to military time?

After the pre-processing you did with your regexes, you can implement if/else logic here by using str_detect()

x <- ifelse(str_detect(x, "\\."),
            as.integer(as.numeric(x) * 2400),
            as.integer(x)) %>% 
  sprintf("%04d", .)

This will return your desired output as character

Then you could do something like this to parse it to POSIXct

x <- as.POSIXct(x,
         format = "%H%M",
         origin = "1970-01-01",
         tz = "UTC")

I followed your logic literally and got the exact same result.

1. Numeric conversion
2. Multiply by 2400 and back to character
3. for loop to detect dots in the character and delete after that
4. for loop to put 0 in front of numbers with less than 4 characters

x <- c("0.9305555555555547", "15:20 Found", "10:00:00 AM Found", "0.125", "Found 1525")

x <- str_extract(x, "[0-9]+.+[0-9]|[0-9][0-9][:][0-9][0-9]")
x <- str_remove(x, "[:]") 
x <- str_remove(x, "[:][0-9][0-9]$")

x <- as.numeric(x)

x <- as.character(ifelse(x<1,x*2400,x))

for(i in 1:length(x)){
  
  ii <- stri_locate_first_regex(x[i],"\\.")[1]
  
  if(!is.na(ii)){
    
    x[i] <- str_sub(x[i],1,ii-1)
    
  }
  
}

for(i in 1:length(x)){
  
  while (nchar(x[i])<4) {
    
    x[i] <- paste0("0",x[i])
    
  }
  
}

x
[1] "2233" "1520" "1000" "0300" "1525"
>

Edit: I realized this:

the decimals need to be multiplied by 2400 to get back to military time

Isn't quite right. "2400" isn't a decimal number (technically it's sexagesimal, base 60), so decimal multiplication won't give a correct result. I've changed my code accordingly.

Rather than using the same regex on everything right out the gate, I would first determine the format of each element of x, then process the element accordingly.

I like the hms library for working with times and use it below, but you could also use the base POSIXct or POSIXlt class.

library(tidyverse)
library(hms)

x <- c("0.9305555555555547", "15:20 Found", "10:00:00 AM Found", "0.125", "Found 1525")

# ----
# define functions for parsing each possible format in `x`
parse_decimal <- function(x) {
  hrs <- as.numeric(str_extract(x, "^0\\.\\d+")) * 24
  min <- (hrs %% 1) * 60
  hrs <- floor(hrs)
  hms(hours = hrs, minutes = min)
}
  
parse_timestring <- function(x) {
  out <- str_remove_all(x, "\\D")
  hr_digits <- if_else(str_length(out) == 3, 1, 2)
  hrs <- as.numeric(str_sub(out, end = hr_digits))
  hrs <- if_else(str_detect(str_to_upper(x), "P\\.?M"), hrs + 12, hrs)
  min <- as.numeric(str_sub(out, start = hr_digits + 1))
  hms(hours = hrs, minutes = min)
}

# ----
# test each element of x, and pass to appropriate parsing Fx
time <- case_when(
  str_detect(x, "^[01]$|^0\\.\\d") ~ parse_decimal(x),
  str_detect(x, "\\d{1,2}:?\\d{2}") ~ parse_timestring(x),
  TRUE ~ NA_real_
)

time
# 22:20:00.000000
# 15:20:00.000000
# 10:00:00.000000
# 03:00:00.000000
# 15:25:00.000000

We should extend the regex for AM/PM indicators so that the forces do not miss each other. Next, in subsets we handle decimal time, imperial time, 24h time, and return the result.

milt <- function(x) {
  u <- trimws(gsub('\\D*(\\d*\\W?[AP]?M?)\\D*', '\\1', x))
  u[grep('\\.', u)] <- sprintf('%04d', round(as.double(u[grep('\\.', u)])*2400))
  u[grep('[AP]M', u)] <- strftime(strptime(u[grep('[AP]M', u)], '%I:%M:%S %p'), '%H%M')
  u[grep(':', u)] <- gsub(':', '', u[grep(':', u)] )
  return(u)
}

milt(x)
# [1] "2233" "1520" "1000" "2200" "0300" "1525" "0000" "1020"

Data:

x <- c("0.9305555555555547", "15:20 Found", "10:00:00 AM Found",
       "10:00:00 PM Found", "0.125", "Found 1525", "0000", "10:20")